Question

the perimeter of a square is 36 inches. find the length of a diagonal. round your answer to the nearest tenth.
the length of the diagonal is about
inches.

Explanation:

Step1: Find side length of square

Perimeter of square \( P = 4s \), where \( s \) is side length. Given \( P = 36 \) inches, so \( 36 = 4s \). Solving for \( s \), we get \( s=\frac{36}{4}=9 \) inches.

Step2: Find diagonal using Pythagorean theorem

In a square, diagonal \( d \) and two sides form a right triangle. So \( d^{2}=s^{2}+s^{2}=2s^{2} \). Substituting \( s = 9 \), we have \( d^{2}=2\times9^{2}=2\times81 = 162 \). Then \( d=\sqrt{162}\approx12.7 \) inches (rounded to nearest tenth).

Answer:

12.7