Problema Solution
A rectangular piece of metal is 25 inches longer than it is wide.Squares with sides 5 inches long are cut from the four corners and the flaps are folded upward to for an open box. If the volume of the box is 930 in^3, what were the original dimensions of the piece of metal?
What is the original width?
What was the original length?
Answer provided by our tutors
let
l = the length of the rectangular metal piece before the cut
w = the width of the rectangular metal piece before the cut
a rectangular piece of metal is 25 inches longer than it is wide
l = 25 + w
the dimensions of the box are:
length: l - 2*5 = l - 10
width: w - 2*5 = w - 10
height: h = 5 in
the volume of the box is V = 930 in^3
V = length*width*height
V = (l - 10)(w - 10)*5
(l - 10)(w - 10)*5 = 930
plug l = 25 + w into the last equations
(25 + w - 10)(w - 10)*5 = 930
by solving we find
w = 16 in
click here to see the step by step solution of the equation
l = 25 + 16
l = 41 in
the original length was 41 inches.
the original width was 16 inches.