Story problem in algebra

Question

A construction company is digging  basement for a house. The length is 45 feet more than the width, and the height is 19 feet less than the width. If the volume of the basement is 24,750 cubic feet, find the dimensions of the basement.

Answer 1

w = width

L = length = w + 45

h = height = w - 19

volume = Lwh = 24750

 

w(w+45)(w-19) = 24750

w³ + 26w² - 855w = 24750

w³ + 26w² - 855w - 24750 = 0

 

w = 30 ft

 

Note:  Realizing that w must be more than 19 or the answer would be negative, 

I plugged in 20 for w in w(w+45)(w-19) = 24750

and that wasn't high enough so I tried w = 30 and that was correct.

 

L = w+45 = 75 ft

h = w-19 = 11 ft

 

Check:  LWH = 24750

75(30)(11) = 24750

24750 = 24750

Answer is verified