Question

10. The sides of rectangle are 12 m and 16 m. What is the length of its diagonal?​

Answer 1

Answer :–

• Length of the diagonal of a rectangle = 20m.

Given :–

• First side of a rectangle = 12 m.
• Second side of a rectangle = 16 m.

To Find :–

• The length of the diagonal of a rectangle.

Solution :–

Let,

The rectangle ABCD.

According to the question,

A rectangle has a diagonal so, the rectangle devides into 2 triangles.

In ∆BCD,

• a = BC = 12 m.

• b = CD = 16 m.

• c = BD = ?

So, we need to find the value of BD (c) (Diagonal),

By the pythagoras theorem,

$\rightarrow {c}^{2} = {a}^{2} + {b}^{2}$

Now, substitute the given values in the pythagoras theorem,

$\rightarrow {c}^{2} = {(12 \: m)}^{2} + {(16 \: m)}^{2}$

$\rightarrow {c}^{2} = 144 \: {m}^{2} + 256 \: {m}^{2}$

$\rightarrow {c}^{2} = 400 \: {m}^{2}$

$\rightarrow c = \sqrt{400 \: {m}^{2} }$

We know that,

• √400 = 20.
• Square root cuts the power.

So,

$\rightarrow c = 20 \: m$

Hence,

The length of the diagonal of a rectangle is 20m.