Question

The volume of the carton is 200 cubic inches. The base of the carton is square and the height is 3 inches more than the length of the base. What are the dimension of the carton?

Answer 1

5. 5 . 8

Explanation:

Volume = 200 cubic inches

Length = x

Base is also same as length = base = x

Height is 3 inches more than the length of the base

h = 3+x

Volume = length x Base x Heigth

V= l x b x h

Put values of l, b and h in above equation, we have

200 = x.x.(x+3)

Let arrange it,

x.x.(x+3) =200

`x^(2)(x+3)=200`

`x^(3)+ 3x^(2) -200 =0\\`

There are multiple ways to solve the cubic equation. Here i use synthetic division other part of answer is available in attached file.