Question

Find the perimeter of a square, the sum of the length of whose diagonals is 144cm.

Answer 1

Answer:

Perimeter of square is 144√2 cm

Step-by-step explanation:

We know that Length of diagonal of a square in terms of side = side × √2

the sum of the length of whose diagonals = 144cm

let the side of square is a cm

Then diagonal is a√2

and according to the question

$a \sqrt{2} + a \sqrt{2} = 144 \\ \\ 2 \sqrt{2} a = 144 \\ \\ a = \frac{144}{2 \sqrt{2} } \\ \\ a = \frac{72}{ \sqrt{2} } \\ \\ = \frac{72 \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } \\ \\ = \frac{72 \sqrt{2} }{2} \\ \\ a= 36 \sqrt{2} \: cm$

So perimeter of a square is

$= 4a \\ \\ = 4 \times 36 \sqrt{2} \\ \\ = 144 \sqrt{2} \: cm$

Hope it helps you.

Answer 2

Step-by-step explanation:

4×36√2=144√2

this is my explanation