Question

If the sum of the lengths of diagonals of a square is 12 √2 cm, find its perimeter.

Answer 1

Given ,

the sum of the lengths of diagonals of a square is 12 √2 cm

We know that , The diagonal of square is given by

Diagonal of square = a√2

Thus ,

a√2 + a√2 = 12√2

2(a√2) = 12√2

a = 6 cm

Therefore ,

• The side of square is 6 cm

Now , the perimeter of square is given by

Perimeter = 4a

Thus ,

Perimeter = 4 × 6

Perimeter = 24 cm

$\sf \therefore \underline{The \: perimeter \: of \: square \: is \: 24 \: cm}$