Question

45-45-90

• the perimeter of a square is 60 inches. find the length of the diagonal

multiple-choice question
what is the length of the diagonal?
options:
$\frac{15}{sqrt{2}}$
$15sqrt{2}$
15
rewatch

Explanation:

Step1: Find side length of square

Perimeter of square is \( 60 \) inches. Formula for perimeter of square: \( P = 4s \), where \( s \) is side length.
So, \( 4s = 60 \) → \( s = \frac{60}{4} = 15 \) inches.

Step2: Use 45-45-90 triangle ratio

The diagonal of a square forms a 45-45-90 triangle with two sides. In a 45-45-90 triangle, hypotenuse (diagonal) \( = s\sqrt{2} \).
Substitute \( s = 15 \): diagonal \( = 15\sqrt{2} \) inches.

Answer:

\( 15\sqrt{2} \) (corresponding to the option with \( 15\sqrt{2} \))