Question

What is the perimeter of a square if the length of one of the diagonals is 12 cm?

6v2 cm
2412 cm
48 cm
24 cm

Answer 1

Explanation:

Use Pythagorean theorem to find the length of the square.

Length of the square = a

a² +a² = diagonal²

2a² = 12²

2a² = 144

a² = 144 ÷ 2

a² = 72

`a =√(72)\\\\ = √(2*2*2*3*3)\\\\ = 2*3√(2)\\\\a = 6√(2)\\\\\\\\Perimeter= 4a\\\\ = 4*6√(2)\\\\= 24√(2) cm`