Question

You are designing a rectangular swimming pool that is to be sent into the ground. The width of the pool is 5 feet more than the depth, and the length is 35 feet more than the depth. The pond holds 2000 cubic feet of water, What are the dimensions of the pool?

Answer 1

Answer:  depth = 5 ft

width =  10 ft

length =  40 ft

Step-by-step explanation:

d =  depth

width = d + 5

length = d + 36

Volume = length x width x depth = 2000 cf

d(d+35)(d+5) = 2000

d($d^{2}$ + 40d + 175) = 2000

d^3 + 40d^2 + 175d = 2000

rewrite in standard cubic polynomial form : ax3 + bx2 + cx + d = 0

d^3 + 40(d^2) + 175d - 2000 = 0

Find the roots of the cubic polynomial:

factors of 2000 are 1, 5, 10 15, 20, etc.

Try the factor 5 first by plugging it in the equation:

5^3 + 40(5^2) + 175(5) - 2000 = 0  

Lucky break!  No need to find the other roots because they will be negative, and you can't have a negative value for a pool depth.

So, depth = 5 ft

width = 5 + 5 = 10 ft

length = 5 + 35 = 40 ft