SOLUTION: The length of a rectangular box is one inch greater than its width. the height is three times the length. The diagonal of the box exceeds the height by one inch find the volume of

Algebra ->  Volume -> SOLUTION: The length of a rectangular box is one inch greater than its width. the height is three times the length. The diagonal of the box exceeds the height by one inch find the volume of       Log On


   

Question 143141: The length of a rectangular box is one inch greater than its width. the height is three times the length. The diagonal of the box exceeds the height by one inch find the volume of the box.
I know what everything equals I just dont know how to solve it algebracally.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x=width

"The length of a rectangular box is one inch greater than its width" __ x+1

"the height is three times the length" __ 3(x+1) __ 3x+3

"The diagonal of the box exceeds the height by one inch" __ 3x+3+1 __ 3x+4

x^2+(x+1)^2+(3x+3)^2=(3x+4)^2 __ x^2+x^2+2x+1+9x^2+18x+9=9x^2+24x+16

subtracting 9x^2+24x+16 __ 2x^2-4x-6=0 __ dividing by 2 __ x^2-2x-3=0

factoring __ (x-3)(x+1)=0 __ x=3 and x=-1 __ negative value not realistic

volume __ x(x+1)(3x+3) __ 3(4)(12) __ 144