Quadratic equations and algebraic expressions

Question

the length of a base of a rectangular prism is 2m more than its width, and the height of the prism is 15m.

a)write an algebraic expression for the volume of the rectangular prism

b) the volume of the prism is 2145m³. Write an equation to model the situation.

c)solve the question in part b) by factoring. What are the dimensions of the base of the prism?

Answer 1

Let's first write expressions for width, length, and height:

 

width = w

length = w + 2

height = 15

 

Since volume = length×width×height, you can plug in those numbers and simplify to find an expression for volume:

 

V = (w+2)(w)(15)

V = (w²+2w)(15)

V = 15w² + 30w

 

 

Since the volume is 2145 m³, plug in V = 2145:

 

2145 = 15w² + 30w

 

 

Finally, rearrange that equation into quadratic form and factor to solve for w:

 

0 = 15w² + 30w - 2145

0 = 15(w² + 2w - 143)

0 = w² + 2w - 143

0 = (w - 11)(w + 13)

w = 11 or -13

 

Since width can't be negative, that means width = 11 m. So, length = w+2 = 11+2 = 13 m.