Answer:
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
Solve for <em>w</em>. Distribute:
Subtract 108 from both sides:
Since the equation is not factorable, we can use the quadratic formula:
In this case, <em>a</em> = 1, <em>b</em> = 8, and <em>c</em> = -108. Substitute and evaluate:
So, our two solutions are:
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.