Problema Solution
A rectangular price of metal is 25 in longer than it is wide. Squares with sides 5in long are cut from the four corners and the flaps are folded upward to for and open box. If the box is 2470 in^3 what were the original dimensions of the piece of metal?
Answer provided by our tutors
let
x = the width of the rectangular piece of metal, x>0
x + 25 = the length of the rectangular piece of metal
after cutting the 5 in from the corners the dimensions of the box are:
x - 10 = width of the box
x + 25 - 10 = x + 15 the length of the box
5 in = the height of the box
the volume of the box is length*width*height that is
(x - 10)(x + 15)*5 = 1470
by solving the quadratic equation we find
x = 18.72 in
click here to see the step by step solution of the quadratic equation
x + 25 = 18.72 + 25 = 43.72 in
the length of the original piece is 43.72 in.
the width of the original piece is 18.72 in.