CTET & State TET Exam > CTET & State TET Questions > The diagonal of a rectangle is 17 cm and its ...
Start Learning for Free
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____
- a)23 cm
- b)32 cm
- c)30 cm
- d)46 cm
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The peri...
Given:
The diagonal of a rectangle = 17 cm
The area of the rectangle = 120 cm2
Formula used:
The diagonal of a rectangle = √(Length2 + Width2)
The area of a rectangle = Length × Width
The perimeter of a rectangle = 2 (Length + Width)
Calculation:
Let, the length of the rectangle = L
The width of the rectangle = W
Then, L × W = 120 .....(1)
Also, √(L2 + W2) = 17
⇒ (L2 + W2) = 172 [Squaring on both sides]
⇒ (L2 + W2) = 289
⇒ (L + W)2 - 2 × L × W = 289 [By using a2 + b2 = (a + b)2 - 2ab formula]
⇒ (L + W)2 - 2 × 120 = 289 [From the equation (1), L × W = 120]
⇒ (L + W)2 - 240 = 289
⇒ (L + W)2 = 289 + 240
⇒ (L + W)2 = 529
⇒ (L + W) = √529 [Taking square root of both sides]
⇒ (L + W) = 23 .....(2)
Now, The perimeter of the rectangle = 2 (L + W)
= 2 × 23 [∵ (L + W) = 23]
= 46 cm
∴ The perimeter of the rectangle is 46 cm.
The diagonal of a rectangle = 17 cm
The area of the rectangle = 120 cm2
Formula used:
The diagonal of a rectangle = √(Length2 + Width2)
The area of a rectangle = Length × Width
The perimeter of a rectangle = 2 (Length + Width)
Calculation:
Let, the length of the rectangle = L
The width of the rectangle = W
Then, L × W = 120 .....(1)
Also, √(L2 + W2) = 17
⇒ (L2 + W2) = 172 [Squaring on both sides]
⇒ (L2 + W2) = 289
⇒ (L + W)2 - 2 × L × W = 289 [By using a2 + b2 = (a + b)2 - 2ab formula]
⇒ (L + W)2 - 2 × 120 = 289 [From the equation (1), L × W = 120]
⇒ (L + W)2 - 240 = 289
⇒ (L + W)2 = 289 + 240
⇒ (L + W)2 = 529
⇒ (L + W) = √529 [Taking square root of both sides]
⇒ (L + W) = 23 .....(2)
Now, The perimeter of the rectangle = 2 (L + W)
= 2 × 23 [∵ (L + W) = 23]
= 46 cm
∴ The perimeter of the rectangle is 46 cm.
Free Test
FREE
| Start Free Test |
Community Answer
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The peri...
Diagonal is 17 cm, then we check the triplet
⇒ 15, 8 and 17
Perimeter = 2 (15 + 8) = 46 its verify, then area
Area rectangle = 2[(1/2)× 15 × 8]
Area = 120 m2
∴ The area of rectangle is 120 m2
⇒ 15, 8 and 17
Perimeter = 2 (15 + 8) = 46 its verify, then area
Area rectangle = 2[(1/2)× 15 × 8]
Area = 120 m2
∴ The area of rectangle is 120 m2
Attention CTET & State TET Students!
To make sure you are not studying endlessly, EduRev has designed CTET & State TET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CTET & State TET.
|
Explore Courses for CTET & State TET exam
|
|
Similar CTET & State TET Doubts
Top Courses for CTET & State TETView all
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer?
Question Description
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer?.
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CTET & State TET.
Download more important topics, notes, lectures and mock test series for CTET & State TET Exam by signing up for free.
Here you can find the meaning of The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The diagonal of a rectangle is 17 cm and its area is 120 cm2. The perimeter of the rectangle is ____a)23 cmb)32 cmc)30 cmd)46 cmCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice CTET & State TET tests.
|
|
Explore Courses for CTET & State TET 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