A rectangular prism's height is x+1. its volume is x^3+7x^2+15x+9. If height and width of the prism are equal, what is its width?

1 Answer
Jan 3, 2017

Width of the prism is 4 units.

Explanation:

As the volume of a rectangular prism, whose length is l, height is h and width is w is lxxhxxw.

As the volume of rectangular prism is x^3+7x^2+15x+9,

and height is (x+1) and width and height being same, height too is (x+1)

we can have its length by dividing x^3+7x^2+15x+9 by (x+1)(x_1)=x^2+2x+1.

Dividing x^3+7x^2+15x+9 by (x^2+2x+1),

x(x^2+2x+1)+5(x^2+2x+1)+4x+4

But as volume is lxxhxxw, 4x+4=4(x+1) too should be a multiple of x^2+2x+1=(x+1)^2,

which is possible if x+1=4 i.e. x=3

Hence width is 4 and height too is 4

Note that volume is 3^3+7xx3^2+15xx3+9=27+63+45+9=144

and length is 144/(4xx4)=9.