In order to solve this, I will set the width equal to W and the length equal to W + 5. We can do this because we know that the length is 5 m more than the width. Because the formula for the area of a rectangle is length * width = area, we can set up this equation.
W * (W + 5) = 176
Now, we solve for W. We start by distributing the W.
[tex] W^{2} + 5W=176[/tex]
Next, we subtract 176 from both sides.
[tex]W ^{2} +5W-176=0[/tex]
Now, we factor this equation. When factored, our equation becomes:
[tex](W-11)(W+16)=0[/tex]
The answers to this equation are:
W = 11, -16
The length can not be -16 meters, so it has to be positive 16 meters. So, the length of this rectangle is 16 meters.
