Question

a square garden has a diagonal of 12 m. What is the perimeter of the garden? Express in simplest radical form

Answer 1

Answer:

The perimeter of the garden, in meters, is $24\sqrt{2}$

Step-by-step explanation:

Diagonal of a square:

The diagonal of a square is found applying the Pythagorean Theorem.

The diagonal of the square is the hypothenuse, while we have two sides.

Diagonal of 12m:

This means that $d = 12$, side s. So

$s^2 + s^2 = 12^2$

$2s^2 = 144$

$s^2 = \frac{144}{2}$

$s^2 = 72$

$s = \sqrt{72}$

Factoring 72:

Factoring 72 into prime factors, we have that:

72|2

36|2

18|2

9|3

3|3

1

So

$72 = 2^{3}*3^{2}$

So, in simplest radical form:

$s = \sqrt{72} = \sqrt{2^{3}*3^{2}} = \sqrt{2^3}*\sqrt{3^2} = 2\sqrt{2}*3 = 6\sqrt{2}$

Perimeter of the garden:

The perimeter of a square with side of s units is given by:

$P = 4s$

In this question, since $s = 6\sqrt{2}$

$P = 4s = 4*6\sqrt{2} = 24\sqrt{2}$

The perimeter of the garden, in meters, is $24\sqrt{2}$