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? 84 feet 42 feet 60 feet 32 feet

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the length and width of the rectangle are the two legs, and the diagonal (hose length) is the hypotenuse. We use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 48 \), \( b = 36 \).

Step2: Calculate \( a^2 \) and \( b^2 \)

\( a^2 = 48^2 = 2304 \), \( b^2 = 36^2 = 1296 \)

Step3: Sum the squares

\( a^2 + b^2 = 2304 + 1296 = 3600 \)

Step4: Take the square root

\( c = \sqrt{3600} = 60 \)

Answer:

60 feet