Question

a hose for a sprinkler system lies along one diagonal of a square garden. the exact length of the hose is $25\sqrt{2}$ feet. what is the perimeter of the garden? explain your reasoning.

Explanation:

Step1: Recall square diagonal formula

For a square with side length \( s \), diagonal \( d = s\sqrt{2} \).

Step2: Find side length from diagonal

Given \( d = 25\sqrt{2} \), set \( s\sqrt{2}=25\sqrt{2} \). Divide both sides by \( \sqrt{2} \), get \( s = 25 \) feet.

Step3: Calculate perimeter of square

Perimeter \( P = 4s \). Substitute \( s = 25 \), so \( P = 4\times25 = 100 \) feet.

Answer:

The perimeter of the garden is 100 feet.