Question

iv) Find the side and perimeter of a square whose diagonal is 10 cm​

Answer 1

Given : Diagonal = 10cm

square is right angled at all vertices so

we can take any triangle made by the diagonal

let the two sides be sides AB and AC and let the diagonal be BC ( I am not abusing )

By using Pythogorus threorem , we can say that

Since all the sides of a square are equal then we can say that AB = AC

AB ² + AC ² = BC ²

AB ² + AB ² = BC ²

2AB ² = BC ²

$ab {}^{2} = \frac{10 {}^{2} }{2}$

$ab = \sqrt{ \frac{10{}^{2} }{2} }$

$ab = \frac{10}{ \sqrt{2} }$

So AB = AC

Therefore each side of this square =

$sides = \frac{10}{ \sqrt{2} }$

Perimeter = 4× side

$4 \times \frac{10}{ \sqrt{2} }$

$perimeter = \frac{40}{ \sqrt{2} } cm$