SOLUTION: A rectangular lot, whose area is 210 meter square, has one of its longer sides next to a river. The total length of fence surrounding the lot is 42 meter. Find the dimensions of

Question 159213: A rectangular lot, whose area is 210 meter square, has one of its longer sides next to a river. The total length of fence surrounding the lot is 42 meter. Find the dimensions of the lot.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!

You are told the area is 210.

You are also told one side of the lot doesn't have a fence; it has a river.
The Fencing is 42.
Normally the perimeter of a rectangle is given by
However, in this case, one of the length sides is on the river. So, the total fencing perimeter is given by

Substitute this value for L back into the Area equation

Use the quadratic equation to solve

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=21 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 12.7912878474779, 8.20871215252208. Here's your graph:

So you have two possible answers for the width. Width is either 8.2 or 12.8
Use the Perimeter equation to find values for Length at each of these values fro width.
If width = 8.2, then =
If width = 12.8, then =
Since the Length in both cases is longer than the width, you lot can be either
16.4 by 12.8 or 25.6 by 8.2 meters

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