Question

45-45-90

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

perimeter is the length all around shape. what is the length of each side?
20 in
15 in
15√2 in
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Explanation:

Step1: Find side length of square

A square has 4 equal sides. Let the side length be \( s \). The perimeter \( P \) of a square is \( P = 4s \). Given \( P = 60 \) inches, we solve for \( s \):
\( 4s = 60 \)
Divide both sides by 4: \( s = \frac{60}{4} = 15 \) inches.

Step2: Find diagonal of square

A square’s diagonal forms a 45-45-90 triangle with two sides. In a 45-45-90 triangle, the diagonal (hypotenuse) is \( s\sqrt{2} \), where \( s \) is the side length. Substituting \( s = 15 \):
Diagonal \( = 15\sqrt{2} \) inches.

Answer:

The length of the diagonal is \( 15\sqrt{2} \) inches (corresponding to the option "15√2 in").