Question

An architect is designing a swimming pool with a base in the shape of a right triangle. According to the architect the pools depth should be 6 feet less than its length, x and its width should be 8 feet less than its length. The volume of water in the pool cannot exceed 1680 ft.³ which statements about the pool are true?

Answer 1

Answer:

Depth = 14 ft Length = 20 ft width = 12 ft

Step-by-step explanation:

Given that an architect is designing a swimming pool

Let length = x

width = x-8

Height = x-6

Then volume of swimming pool = base area x height

base area = area of triangle = $\frac{1}{2} x(x-8)$

Volume = $\frac{1}{2} x(x-8)(x-6)=1680$

Solving we find that x=20

Verify:

Length = 20: Width = 12: and height = 14

Volume = 1/2 (20)(12)(14) = 1680 ft ^3