Question

the area of square is 100cm2 the length of its daigonal will be​

Answer 1

Given:

A square with

• Area = 100 cm²

What To Find:

We have to find the diagonal of the square.

How To Find:

To find it, we have to

• First find we have to the side of square.
• Then, find the diagonal of the square.

Formula:

• Area of the square = side²
• Diagonal of the square =  $\sf{\sqrt{2}s}$ where s = side.

Solution:

• FInding the side of the square.

Using the formula,

⇒ Area = side²

Substitute the value,

⇒ 100 cm² = side²

Take the square to LHS,

⇒ $\sf{\sqrt{100} = side}$

Find the square root of 100,

⇒ 10 cm = side

∴ Thus, side is 10 cm.

• Finding the diagonal of the square.

Using the formula,

⇒ $\sf{Diagonal = \sqrt{2} s}$

Subtitute the value,

⇒ $\sf{Diagonal = \sqrt{2} \times 10}$

Assume √2 ≈ 1.414,

⇒ Diagonal = 1.414 × 10

Multiply the numbers,

⇒ Diagonal = 14.14 cm

∴ Thus, the diagonal is 14.14 cm.