Question

Find the diagonal of a square whose sides are of the given measure. Given = 3sqrt2

Answer 1

ANSWER

The diagonal of the square is 6 units.

EXPLANATION

A diagonal of a square divides the square into two congruent right isosceles triangles.

Let the sides of the square be 's' units. Then, the Pythagoras Theorem says that, the sum of the squares of the shorter legs will be equal to the square of the hypotenuse.

Let the diagonal which is the hypotenuse be 'd' units.

Then,

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

$\implies \: {d}^{2} = 2{s}^{2}$

From the question, the side length of the square is

$s = 3 \sqrt{2} \: units$

We plug in this value to obtain:

$\implies \: {d}^{2} = 2{(3 \sqrt{2} )}^{2}$

Or

$\implies \: {d}^{2} = 2 \times { {3}^{2} (\sqrt{2} )}^{2}$

$\implies \: {d}^{2} = 9 \times 2 \times 2 = 36$

We take the positive square root of both sides to get:

$d = \sqrt{36}$

$d = 6 \: units$