SOLUTION: A rectangular pen is 3 feet longer than its wide. Give the possible values for the width W of the pen if its area must be between 154 and 460 inclusively. I'm bad enough at geomet

Question 453088: A rectangular pen is 3 feet longer than its wide. Give the possible values for the width W of the pen if its area must be between 154 and 460 inclusively.
I'm bad enough at geometry, but I actually thought I was getting the hang of finding areas until I saw this problem. Can someone help please? I've never even seen anything like this before. Thanks
Answer by Sarpi(32) (Show Source): You can put this solution on YOUR website!
Let x= the width and therefore length= 3+x
Area= L*W = (3+x)*x
So by simple simplification, the area has the equation,
We are bounded to find values of width within the areas of 154 and 460. Which means this equation must hold true,
we solve two equations:
...... eqn 1
..... eqn 2
The two equations have a quadratic system that is
Eqn 1: using this formula
will give that is:
Eqn 2: also with the formula gives that is:
Note: The areas 154 and 460 are included and we deal with positive values because we are looking for measurements.
So we have 11 and 20 from eqn 2 and 1 respectively. However, the possible values for the Width in order to find the areas between 154 and 460 ranges from 11 to 20.
Mathematically: is the solution, 11 and 20 are included.

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