SOLUTION: The dimensions 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 remains t

Algebra ->  Rectangles -> SOLUTION: The dimensions 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 remains t      Log On


   

Question 987440: The dimensions 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 remains the same, the new volume is 34 cmcube more than the original volume. what is the new dimension of the enlarged rectangular metal box?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Original volume, 3%2A5%2A8%2Acm%5E3.

New volume using some added x to the first two dimensions, %283%2Bx%29%285%2Bx%29%2A8=3%2A5%2A8%2B34.
You essentially want to find x, the length addition to the first two dimensions.

STEPS TOWARD SOLUTION
%283%2A5%2B5x%2B3x%2Bx%5E2%298=3%2A5%2A8%2B34
3%2A5%2A8%2B64x%2B8x%5E2=3%2A5%2A8%2B34
8x%5E2%2B64x=34
highlight_green%284x%5E2%2B32x-17=0%29


Formula for general solution of a quadratic equation....
Discriminant=32%5E2%2B4%2A4%2A17=1296=highlight_green%2836%5E2%29

x=%28-32%2B36%29%2F%282%2A4%29

x=4%2F%282%2A4%29
highlight%28x=1%2F2%29------the length added each to 3 and the 5.