Question

if the diagnol of a square is 8cm. find
length
perimeter
area ​

Answer 1

To Find:-

• Area and Perimeter

Given:-

Diagonal:- 8cm

Solution:-

We know

In a square all angles are equal,and each are of 90°

therefore

Consider ∆ABC

where a=90°

We know

In a right triangle,The Longest side(side opposite to 90°) known As Hypotenuse can be find out through Pythagoras Theorem that is

Hypotenuse² = s²+s²)

Where s & s are the remaining two sides of a triangle

Here

BC= Hypotenuse

AB & AC = remaining sides

Therefore

BC²=AB²+AC²

Since it's a square,then AB=AC,

that is

8²=s²+s²=2s²

2s²=64

s²=64÷2=32

s=√32

s=4√2

Therefore the length of one side= 4√2cm

• Now to Find Perimeter

we know

Perimeter of a square= 4s

where s=semi perimeter

that is

4×4√2

16√2

Therefore the perimeter is 16√2cm

• Now To Find Area

We know

Area of a square= s²

substituting the value

that is

Area= (4√2)²

Area=16×2=32cm²

Therefore the Area is 32cm²

Hope it helps

Hit The Brainliest if you find it helpful