Question

find the perimeter of a square whose diagonal.
is
10 √2 cm
​

Answer 1

Step-by-step explanation:

by Pythagoras theorm

H²=B²+P²

10√2×10√2=s²+s²

100×√2²=2s²

100×2=2s²

200/2=s²

100=s²

s=10

so each side of a square is equal to 10cm

perimeter=4×side

=4×10

=40cm

hope this will help you

Answer 2

Given :

• Diagonal of the square =$\tt{10 \sqrt{2} cm}$

To Find :

• The perimeter of a square =?

Formula :

•Pythagoras Theorem :

>> H²=B²+P²

Solution :

Let each side of the square measure be s

According to Pythagoras Theorem :

$\\ \\ \implies\displaystyle\sf{H^{2}=B^{2}+P^{2}}$

$\\ \\ \implies \displaystyle \sf \: {(10 \sqrt{2} )}^{2} = {s}^{2} + {s}^{2} \\ \\ \\ \implies \displaystyle \sf \: (10 \times 10 \times \sqrt{2} \times \sqrt{2} ) = 2 {s}^{2} \\ \\ \\ \implies \displaystyle \sf \: 200 = 2 {s}^{2} \\ \\ \\ \implies \displaystyle \sf \: {s}^{2} = \frac{200}{2} \\ \\ \\ \implies \displaystyle \sf \: {s}^{2} = 100 \\ \\ \\ \implies \displaystyle \boxed{ \sf{s = 10cm}}$

So, each sides of the square is 10 cm

$\\ \\ \red\bigstar\bf{Perimeter \: of \: square =4 \times \: side}$

$\\ \\ \implies \displaystyle \sf \: perimeter \: of \: square = 4 \times side \\ \\ \\ \implies \displaystyle \sf \: perimeter \: of \: side = 4 \times 10cm \\ \\ \\ \implies \displaystyle \sf \: perimeter \: of \: square = 40cm$

Hence, the perimeter of the square is 40cm.