Problema Solution
A box with no top is to be formed by taking a rectangular piece of metal 16 by 20 cm and cutting a square of the same size out of each corner and folding up the sides. If the are of the base is to be 96 square cm.What should the lenght of the sides of the squares be?
Answer provided by our tutors
Let "x" be the side of the square cutting from each edge.
Base area =(20-2x)(16-2x).
(20-2x)(16-2x)=96.
320-40x-32x+4x^2=96.
4x^2-72x+320-96=0.
4x^2-72x+224=0.
x^2-18x+56.
(x-14)(x-4)=0.
x=14,4.
Take x=4 cm as x=14 can not be valid as alreday one side is 16cm.
length of the side of the square cut =4cm.