SOLUTION: The dimension of a rectangular metal box are 3 cm, 5 cm, and 8 cm. If the first two dimensions are increased by the same number of centimeters, while the third dimension remain the

Algebra ->  Rectangles -> SOLUTION: The dimension of a rectangular metal box are 3 cm, 5 cm, and 8 cm. If the first two dimensions are increased by the same number of centimeters, while the third dimension remain the      Log On


   

Question 989463: The dimension of a rectangular metal box are 3 cm, 5 cm, and 8 cm. If the first two dimensions are increased by the same number of centimeters, while the third dimension remain the same, the new volume is 34cm to the third power more than the original volume. What is the new dimension of the enlarged rectangular metal box?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of the new box:
%283%2Bx%29%285%2Bx%298, 34 cubic cm more volume than the old box.

%28x%2B3%29%28x%2B5%29%2A8-3%2A5%2A8=34

%28x%5E2%2B8x%2B15%29%2A8-120-34=0
%28x%5E2%2B8x%2B15%29%2A8-154=0
%28x%5E2%2B8x%2B15%29%2A4-77=0
4x%5E2%2B32x%2B60-77=0
4x%5E2%2B32x-17=0

Try directly using formula for general solution of quadratic equation to find x.
Discriminant is ...., 36%5E2.

x=%28-32%2B36%29%2F%282%2A4%29
highlight%28x=1%2F2%29
Find the new dimensions from this.