# Thread: Area of a Rectangle

1. ## Area of a Rectangle

Having trouble with this seemingly simple problem, help is much appreciated!

Three sides of a fence and an existing wall form a rectangular enclosure. The total length of fencing used for the three sides is 240 ft. Let x be the length of each of the two sides perpendicular to the wall.
a. Draw a picture and write a formula for the area of the enclosure.
b. Then find the value for x that would give an area of 5500 ft^2

a. Pictures easy but would the formula for the area of the rectangle be x times y = 5,500?

b. Don't really know how to find the exact value for x, so I just used trial and error to find x to be around 214.35 and y to be around 25.65.

Help with finding the exact value and the formula would be great.

2. $\displaystyle A = L \times W$

where $\displaystyle L = x, W = y$

and we know $\displaystyle 2x+y=240$ so $\displaystyle y= 240-2x$

therefore $\displaystyle A = x\times (240-2x)$

$\displaystyle 5500 = x\times (240-2x)$

$\displaystyle 5500 = 240x-2x^2$

$\displaystyle 0 = 240x-2x^2-5500$