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

A. 8cm

Step-by-step explanation

The diagonal of the square is

`d = 8 √(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 √(2) )^(2)`

`2{l}^(2) = 128`

Solve for l,

`{l}^(2) = 64`

Take positive square root of both sides

`l = √(64)`

`l = 8cm`