Question

The area of the surface of the swimming pool is 210 square feet. What is the length d of the deep end (in feet)?

shallow end

Width-10 ft

length-9 ft

Answer 1

The answer is 3.16 ft

The surface area (SA) of the rectangular prism is:
SA = 2lw + 2ld + 2wd

However, the pool is without the top side, so the area of the top side should be excluded from the surface area of the pool. The surface area of the rectangular pool is:
SA = lw + 2ld + 2wd

We know:
SA = 210 ft²
l = 9 ft
w = 10 ft
d = ?

210 = 9 * 10 + 2 * 9 * d + 2 * 10 * d
210 = 90 + 18d + 20d
210 - 90 = 38d
120 = 38d
d = 120/38
d = 3.16 ft