GATE Exam > GATE Questions > A rectangle becomes a square when its length ...
Start Learning for Free
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?
- a)1125
- b)2250
- c)2924
- d)4500
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A rectangle becomes a square when its length and breadth are reduced b...
Let's assume the original length and breadth of the rectangle as L meters and B meters, respectively.
Reduced Length and Breadth:
According to the question, when the length and breadth are reduced by 10 meters and 5 meters respectively, the rectangle becomes a square. Hence, the reduced length and breadth would be (L - 10) meters and (B - 5) meters, respectively.
Area of the Original Rectangle:
The area of the original rectangle is given by the formula:
Original Area = Length × Breadth = L × B
Area of the Reduced Rectangle:
The area of the reduced rectangle (square) is given by the formula:
Reduced Area = Reduced Length × Reduced Breadth = (L - 10) × (B - 5)
Loss of Area:
According to the question, the rectangle loses 650 m² of area during this process.
Loss of Area = Original Area - Reduced Area = L × B - (L - 10) × (B - 5) = 650
Simplifying the equation, we get:
L × B - L × (B - 5) - 10 × (B - 5) = 650
L × B - L × B + 5L - 10B + 50 = 650
5L - 10B = 600
L - 2B = 120
Since the above equation contains two variables L and B, we need another equation to solve for their values.
Relation between Length and Breadth:
Since the rectangle becomes a square after reducing the length and breadth, we can say that:
L - 10 = B - 5
Simplifying this equation, we get:
L - B = 5
Using the above two equations, we can solve for L and B:
L - 2B = 120
L - B = 5
By subtracting the second equation from the first equation, we get:
L - 2B - (L - B) = 120 - 5
-L + B = 115
B - L = -115
Adding this equation to the equation L - B = 5, we get:
2B = 120
B = 60
Substituting the value of B in the equation L - B = 5, we get:
L - 60 = 5
L = 65
Now, we have the values of L and B. Substituting these values in the equation for the original area, we get:
Original Area = L × B = 65 × 60 = 3900 m²
Hence, the area of the original rectangle is 3900 m², which is not one of the given options. Therefore, there might be an error in the question or the options provided.
Reduced Length and Breadth:
According to the question, when the length and breadth are reduced by 10 meters and 5 meters respectively, the rectangle becomes a square. Hence, the reduced length and breadth would be (L - 10) meters and (B - 5) meters, respectively.
Area of the Original Rectangle:
The area of the original rectangle is given by the formula:
Original Area = Length × Breadth = L × B
Area of the Reduced Rectangle:
The area of the reduced rectangle (square) is given by the formula:
Reduced Area = Reduced Length × Reduced Breadth = (L - 10) × (B - 5)
Loss of Area:
According to the question, the rectangle loses 650 m² of area during this process.
Loss of Area = Original Area - Reduced Area = L × B - (L - 10) × (B - 5) = 650
Simplifying the equation, we get:
L × B - L × (B - 5) - 10 × (B - 5) = 650
L × B - L × B + 5L - 10B + 50 = 650
5L - 10B = 600
L - 2B = 120
Since the above equation contains two variables L and B, we need another equation to solve for their values.
Relation between Length and Breadth:
Since the rectangle becomes a square after reducing the length and breadth, we can say that:
L - 10 = B - 5
Simplifying this equation, we get:
L - B = 5
Using the above two equations, we can solve for L and B:
L - 2B = 120
L - B = 5
By subtracting the second equation from the first equation, we get:
L - 2B - (L - B) = 120 - 5
-L + B = 115
B - L = -115
Adding this equation to the equation L - B = 5, we get:
2B = 120
B = 60
Substituting the value of B in the equation L - B = 5, we get:
L - 60 = 5
L = 65
Now, we have the values of L and B. Substituting these values in the equation for the original area, we get:
Original Area = L × B = 65 × 60 = 3900 m²
Hence, the area of the original rectangle is 3900 m², which is not one of the given options. Therefore, there might be an error in the question or the options provided.
Free Test
FREE
| Start Free Test |
Community Answer
A rectangle becomes a square when its length and breadth are reduced b...
Step 1. Draw a rectangle with a square inscribed in it at one of the corners. This will help us to visualise things properly.
we are taking the side of the square as x.
Step 2. The Length of the rectangle ( L ) will be x + 10 and the breadth ( B ) will be x + 5. This is derived from the given logic that reducing 10 m from Length and 5 m from breadth will result in a square.
Step 3. we can write ( x + 10 ) ( x + 5 ) = 650 + x ^ 2.
area of rectangle = remaining area ( given data ) + area of square.
open up the brackets and cross down the x^2s . the solve for x.
15 x = 600.
x = 40.
=> L = 40 + 10 = 50
=> B = 40 + 5 = 45
L*B = 2250.
we are taking the side of the square as x.
Step 2. The Length of the rectangle ( L ) will be x + 10 and the breadth ( B ) will be x + 5. This is derived from the given logic that reducing 10 m from Length and 5 m from breadth will result in a square.
Step 3. we can write ( x + 10 ) ( x + 5 ) = 650 + x ^ 2.
area of rectangle = remaining area ( given data ) + area of square.
open up the brackets and cross down the x^2s . the solve for x.
15 x = 600.
x = 40.
=> L = 40 + 10 = 50
=> B = 40 + 5 = 45
L*B = 2250.
|
Explore Courses for GATE exam
|
|
Top Courses for GATEView all
Question Description
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer?.
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer?.
Solutions for A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2of area. What is the area of the original rectangle in square meters?a)1125b)2250c)2924d)4500Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily