Height of square pyramid is 5 meters shorter than side of base. Volume is 108 cubic meters. How tall is pyramid?

Question

Algebra II Honors with Trig

Answer 1

V=(a²h/3)

a=side length of the base

a-5=height

108=(a²[a-5])/3

108*3=a²[a-5]

324=a³-5a²

a³-5a²-324=0

zeroes of the equation are factors of 324

324=2*2*3*3*3*3

possible zeroes are 1, 2, 3, 4, 6, 9, 12, ....

9 is a zero

9³-5*9²-324=0

729-405-324=0

a=9 meters, which is the side of the base

9-5=4 meters, which is the height