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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?
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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.
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Community Answer
A rectangle becomes a square when its length and breadth are reduced b...
Let the length and breadth of the rectangle is L and B respectively.
The area of the rectangle = LB
It becomes square when its length and breadth are reduced by 10 m and 5 m, respectively.
Now, the length and breadth of the square become (L – 10) and (B – 5) respectively.
As in a square the length and breadth are the same, L – 10 = B – 5
⇒ L = B + 5
The area of the square = (L – 10) (B – 5)
Given that, the rectangle loses 650 m2 of area
⇒ LB – 650 = (L – 10) (B – 5)
⇒ LB – 650 = LB + 50 – 10B – 5L
⇒ 10B + 5L = 700
⇒ 10B + 5(B + 5) = 700
⇒ B = 45 m
⇒ L = B + 5 = 50 m
Area of the original rectangle = LB = 50 × 45 = 2250 m2
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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?
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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 2024 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 2024 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?.
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