Question 1054231: A rectangular piece of cardboard 11 inches by 14 inches is made into a box by cutting identical squares from each corner and folding up the sides. If the bottom of the box turns out to have an area of 80 in^2, what size squares were cut from the corners?
The equation I am coming up with does not give me an answer that would fit.
Found 2 solutions by Fombitz, jorel555:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! So you fold up a square of size, X, from each edge.
Let's call the left over part A on the width and B on the length so that,
.
.
and the area of the bottom,
So from the length and width,
Substituting,
Complete the square,
Although there are two answers, we are limited by,
which leads to the solution,
Answer by jorel555(1290)  (Show Source):
You can put this solution on YOUR website! Let n be the length of the sides of the squares cut from the box. Then:
(11-2n)(14-2n)=80
154-50n+4nē=80
4nē-50n+74=0
2nē-25n+37=0
Using the quadratic formula, we get n=10.7845892868 or 1.7154107132. Throwing out the higher result, we get the size of the squares to be 1.7154107132 in. x 1.7154107132 in. ☺☺☺☺
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