Question

find the length of the diagonal of a square with perimeter 32. p = 32 a. (4sqrt{2}) b. 8 c. (2sqrt{2}) d. 45 e. (8sqrt{2})

Explanation:

Step1: Find side length of square

Perimeter of square \( P = 4s \), where \( s \) is side length. Given \( P = 32 \), so \( 4s = 32 \). Solving for \( s \), we divide both sides by 4: \( s=\frac{32}{4}=8 \).

Step2: Find diagonal using Pythagorean theorem

In a square, diagonal \( d \) forms a right triangle with two sides. By Pythagorean theorem, \( d^{2}=s^{2}+s^{2} \). Substituting \( s = 8 \), we get \( d^{2}=8^{2}+8^{2}=64 + 64 = 128 \). Taking square root, \( d=\sqrt{128}=\sqrt{64\times2}=8\sqrt{2} \).

Answer:

E. \( 8\sqrt{2} \)