Problema Solution
the width of a rectangle piece of cardboard is 8in. less than its length. a square piece that measures 2in. on each side is cut from each corner, then the sides are turned up to make a box with volume 480in cube. find the length and width of the original piece of a cardboard.
Answer provided by our tutors
let
l = the length of the original piece of a cardboard
w = the width of the original piece of a cardboard
the width of a rectangle piece of cardboard is 8 in less than its length:
w = l - 8
the length of the box is: l - 2*2 = l - 4
the width of the box is: w - 2*2 = w - 4
the height of the box is: h = 2 in
the volume of the box is: 480 in^3
the volume of the box = length*width*height
(l - 4)(w - 4)*2 = 480
plug w = l - 8 into (l - 4)(w - 4)*2 = 480
(l - 4)(l - 8 - 4)*2 = 480
by solving we find:
l = 24 in
click here to see the step by step solution of the equation:
w = l - 8
w = 24 - 8
w = 16 in
the length of the original piece of a cardboard is 24 in.
the width of the original piece of a cardboard is 16 in.