Question

A square garden has a diagonal of 34 ft. Colton wants to put a fence around the entire garden.

Answer 1

The diagonal of a square forms two 45-45-90 triangles.

The ratios of the lengths of the sides of a 45-45-90 triangle are

$1~:~1~:~\sqrt{2}$

The hypotenuse is $\sqrt{2}$ times the length of the legs.

Each leg is the length of the hypotenuse divided by $\sqrt{2}$.

$leg = \dfrac{34}{\sqrt{2}} = 24.0416$

$perimeter = 4 \times side$

$perimeter = 4 \times 24.0416$

$perimeter = 96.166$

Answer: he will need 96.2 ft of fencing.

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