Question

The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 252 cubic inches, find the dimensions of the box. length in width in height in

Answer 1

height be 4 in

length be 9 in

ANd, the width be 7 in

Explanation:

Let us assume the height of the box be x

So the length would be 2x + 1

And, the width be x + 3

As we know that

The volume of the rectangular box = length × width × height

252 = (2x + 1) × (x + 3) × (x)

252 = (2x^2 + x) × (x + 3)

252 = 2x^3 + 6x^2 + x^2 + 3x

2x^3 + 7x^2 + 3x = 252

2x^3 + 7x^2 + 3x - 252 = 0

after solving this

x = 4

So height be 4 in

length be 9 in

ANd, the width be 7 in