Question

a rectangular swimming pool has a length of 48 feet and a width of 36 feet. a hose needs to extend from the southwest corner of the pool to the northeast corner of the pool. what is the shortest length the hose can be to extend from one corner to the other corner? 42 feet 32 feet 84 feet 60 feet

Explanation:

Step1: Identify right - triangle

The length, width and diagonal of the rectangular pool form a right - triangle. The length $a = 48$ feet and width $b = 36$ feet.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the length of the diagonal (the hose length). So $c=\sqrt{48^{2}+36^{2}}$.

Step3: Calculate squares

$48^{2}=48\times48 = 2304$ and $36^{2}=36\times36=1296$. Then $a^{2}+b^{2}=2304 + 1296=3600$.

Step4: Find square root

$c=\sqrt{3600}=60$ feet.

Answer:

D. 60 feet