CAT Exam > CAT Questions > Area of a Rhombus of perimeter 56 cms is 100...
Start Learning for Free
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.
- a)33.40 cm
- b)34.40 cm
- c)34 cm
- d)33 cm
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of ...
To find the sum of the lengths of the diagonals of a rhombus, we need to first find the length of one of the diagonals. Let's assume the length of one diagonal is 'd' and the other diagonal is 'D'.
Given that the perimeter of the rhombus is 56 cm, we can use the formula for the perimeter of a rhombus: 4s, where 's' is the side length of the rhombus.
So, 4s = 56 cm
=> s = 56 cm / 4
=> s = 14 cm
Since the area of the rhombus is given as 100 sq cm, we can use the formula for the area of a rhombus: (d * D) / 2
Given that the area is 100 sq cm, we have:
100 = (d * D) / 2
=> d * D = 200
Now, we have two equations:
1. s = 14 cm
2. d * D = 200
To find the lengths of the diagonals, let's consider the possible pairs of factors of 200:
1, 200
2, 100
4, 50
5, 40
8, 25
10, 20
Since the diagonals of a rhombus intersect at right angles, the lengths of the diagonals must be perpendicular bisectors of each other. Therefore, the lengths of the diagonals must be equal.
From the given options, we can see that the sum of the lengths of the diagonals is 34.40 cm (option B), which corresponds to the pair of factors 4 and 50.
Hence, the correct answer is option B: 34.40 cm.
Given that the perimeter of the rhombus is 56 cm, we can use the formula for the perimeter of a rhombus: 4s, where 's' is the side length of the rhombus.
So, 4s = 56 cm
=> s = 56 cm / 4
=> s = 14 cm
Since the area of the rhombus is given as 100 sq cm, we can use the formula for the area of a rhombus: (d * D) / 2
Given that the area is 100 sq cm, we have:
100 = (d * D) / 2
=> d * D = 200
Now, we have two equations:
1. s = 14 cm
2. d * D = 200
To find the lengths of the diagonals, let's consider the possible pairs of factors of 200:
1, 200
2, 100
4, 50
5, 40
8, 25
10, 20
Since the diagonals of a rhombus intersect at right angles, the lengths of the diagonals must be perpendicular bisectors of each other. Therefore, the lengths of the diagonals must be equal.
From the given options, we can see that the sum of the lengths of the diagonals is 34.40 cm (option B), which corresponds to the pair of factors 4 and 50.
Hence, the correct answer is option B: 34.40 cm.
Free Test
FREE
| Start Free Test |
Community Answer
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of ...
Given, Perimeter = 56 and area = 100.
Let the side of the rhombus be “a", then 4a = 56
⇒ a = 14.
Area of Rhombus = Half the product of its diagonals. Let the diagonals be d1 and d2 respectively.
⇒ d1 * d2 = 200.
By Pythagoras theorem, (d1)2 + (d2)2 = 4a2
⇒ (d1)2 + (d2)2 = 4×196
= 784.
(d1)2 + (d2)2 + 2d1 × d2 = (d1 + d2)2
= 784 + 2 × 200 = 1184
⇒ 
= 34.40
Therefore, sum of the diagonals is equal to 34.40 cm.
Hence, the correct option is (b).
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer?
Question Description
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer?.
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
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 to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup