Question

The diagonal of a square has a length of Eight times begin square root two end square root cm. Find the length of a side of the square. A. 8 cm B. 4 cm C. Two times begin square root two end square root cm D. Five times begin square root two end square root cm

Answer 1

ANSWER

A. 8cm

EXPLANATION

The diagonal of the square is

$d = 8 \sqrt{2} cm$

Let the length of each side of the square be l units.

Then the diagonal and any two sides form an isosceles right triangle with the diagonal being the hypotenuse.

We use the Pythagoras Theorem, to obtain,

${l}^{2} + {l}^{2} = {d}^{2}$

This implies that,

$2 {l}^{2} = (8 \sqrt{2} )^{2}$

$2{l}^{2} = 128$

Solve for l,

${l}^{2} = 64$

Take positive square root of both sides

$l = \sqrt{64}$

$l = 8cm$