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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?
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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.
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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
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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?
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