Question

The length of a rectangle is 16 cm and one of its diagonal is 20 cm. Find the perimeter of the

rectangle ​

Answer 1

Question

• The length of a rectangle is 16 cm and one of its diagonal is 20 cm. Find the perimeter of the rectangle.

Answer

• Perimeter of rectangle is 56 cm.

Step By Step Explanation

Given that:

• Length of rectangle is 16 cm.
• One of it's diagonal is 20 cm.

To Find:

• Perimeter of rectangle?

Solution:

• Firstly let's calculate the breadth of rectangle (b) by using well known formula i.e, formula of diagonal of rectangle :
• $\pmb{\boxed{\bf{\pink{Diagonal = \sqrt{{\ell}^{2} + b^2}}}}}$
• Where, ℓ is length of rectangle and b is breadth of rectangle.

❏ Putting all values in formula :

↦ $\sf 20 = \sqrt{\big(16\big)^2 + \big(b\big)^2}$

↦ $\sf 20 = \sqrt{256 + b^2}$

✭ Squaring both sides :

↦ $\sf \big(20\big)^2 = \big(\sqrt{256 + b^2}\big)^2$

↦ 400 = 256 + b²

↦ b² = 400 - 256

↦ b² = 144

↦ $\sf b = \sqrt{144}$

↦ $\sf b = \sqrt{12\:\times\:12}$

➦ $\pmb{\underline{\boxed{\bf{\purple{Breadth\:(b) = 12\:cm}}}}}$

• Now, let's find perimeter of rectangle by using formula of perimeter of rectangle i.e,
• $\pmb{\boxed{\bf{\green{Perimeter_{(rectangle)} = 2\big(\ell + b\big)}}}}$
• Where, ℓ is length of rectangle and b is breadth of rectangle.

❏ Putting all values in formula :

⇒ $\sf Perimeter_{(rectangle)} = 2\big(16 + 12\big)$

⇒ $\sf Perimeter_{(rectangle)} = 2\big(28\big)$

⇒ $\sf Perimeter_{(rectangle)} = 2\:\times\:28$

➳ $\pmb{\underline{\boxed{\bf{\red{Perimeter_{(rectangle)} = 56\:cm}}}}}$

∴ Hence, the perimeter of rectangle is 56cm.

Know More :

• Perimeter of any figure is calculated by sum of it's sides.
• Perimeter of square = 4 × side
• Perimeter of rectangle = 2(ℓ + b)
• Perimeter of circle = 2πr
• Perimeter of equilateral ∆ = 3 × side

❏ Some related Questions & Answers :

• Ques 1 :

The length of a rectangle is 15 cm greater than its breath. Its perimeter is 150cm. Find the dimensions of the rectangle.

• Ans :

https://brainly.in/question/43278245

• Ques 2 :

A square and a rectangle have the same perimeter. If the side of the square is 16 m and the length of the rectangle is 18 m, the breadth of the rectangle is : (A) 14 m (B) 15 m (C) 16 m (D) 17 m.

• Ans :

https://brainly.in/question/43446860

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Answer 2

Answer:

$\green{ \boxed{ \dag \: \: \bf \: \: perimeter \: \: s = 56 \: cm}}$

Step-by-step explanation:

Given,

• The lenght of a rectangle is l = 16 cm
• diagonal d = 20 cm

To find :

Perimeter of the rectangle = s

Solution :

we know that

perimeter s = 2(length × breadth) = 2(l×b)

But in the question breadth is unknown. So we have to find it.

To find breadth, we will use the following formula .

$\sf \: diagonal \: (d) = \sqrt{ {length(l)}^{2} + {breadth(b)}^{2} } \\ \sf \implies \: d = \sqrt{ {l}^{2} + {b}^{2} } \\ \sf \implies \:20 = \sqrt{ {(16)}^{2} + {b}^{2} } \\ \sf \implies \: {(20)}^{2} = {( \sqrt{256 + {b}^{2} } }) ^{2} \\ \sf \implies \:400 = 256 + {b}^{2} \\ \sf \implies \: {b}^{2} = 400 - 256 = 144 \\ \sf \implies \:b = \sqrt{144} \\ \sf \implies \:b = 12 \: cm \: \\ \\ \pink{\sf \: so \: breadth \: \: b = 12 \: \: cm \: }$

$\sf \: now \: perimeter \: \: s = 2(l + b) \\ \sf = 2(16 + 12) \\ = 2 \times 28 \\ = 56 \: \: cm \: \\ \\ \green{ \boxed{ \sf \: \therefore \: perimeter \: \: s = 56 \: cm}}$