How to find LWH (Algebra)

Question

A rectangular prism has edges of length x, x + 2, and 2x-3 inches. The volume of the prism is 1040 cubic inches. Write a polynomial equation that models the prism's volume. What are the prism's dimensions?

 

How would I find Length, Width, and Height?

Answer 1

x(x+2)(2x-3)=1040

2x^3+x^2-6x=1040

factor 1040

1040=2*2*2*2*5*13

try 13 for x and you will see that it is too large

try 5 for x and you will see that it is too small

try 8 for x

2*8^3+8^2-6*8=1040

1024+64-48=1040

1088-48=1040

1040=1040

x=8 inches, x+2=10 inches, and 2x-3=13 inches

8*10*13=1040 cubic inches