Answer:
For a rectangle of length L and width W, the area is:
A = L*W
In this case, we know that;
The length is 18ft more than the width.
L = W + 18ft
The area is 175 ft^2
Then:
A = 175 ft^2
Then we have a system of two equations:
L = W + 18ft
A = L*W = 175 ft^2
To solve this, the first step would be to replace the first equation into the second one:
(18ft + W)*W = 175ft^2
Now we can solve this for W.
18ft*W + W^2 - 175ft^2 = 0.
This is the quadratic equation, i will solve it just to be complete.
We have a quadratic equation, using the Bhaskara formula we can find the two solutions as:
[tex]w = \frac{-18ft +- \sqrt{(18ft)^2 - 4*1*(-175ft^2)} }{2*1} = \frac{-18ft +- 32ft}{2ft}[/tex]
Then the two solutions are:
W = (-18ft - 32ft)/2 = -25ft (This option can be discarded, because a negative width has no sense)
W = (-18ft + 32ft)/2 = 7ft
Then the width is 7ft long, and the lenght will be:
L = W + 18ft = 7ft + 18ft = 25ft
