Problema Solution
A rectangular piece of cardboard is 15 inches longer than it is wide. A 5 inch square is cut from each corner, and the remaining piece is folded to form a box. If the volume of the box is 1,250 cubic inches, what is the length of the box?
Answer provided by our tutors
Let
x = the width of the box, x>0
x + 15 = the length of the box
The dimensions of the box are:
x - 2*5 = x - 10 the width of the box
x + 15 - 2*5 = x + 5 the length of the box
h = 5 in the height of the box
V = 1,250 in^2 the volume of the box
V = width*length*height
V = (x - 10)(x + 5)*5
(x - 10)(x + 5)*5 = 1250
........
........
x = 20 in
x + 5 = 20 + 5 = 25 in
The length of the box is 25 inches.