Question

The length of a rectangle is six times the width.

if the perimeter of the rectangle is 112 in, find it's area.

? in^2

Answer 1

The area of the rectangle is 1536 in^2.

Explanation:

We can set up a system of equations using the information we have. We can use P=112 and P=2(W+6W), where p is the perimeter and w is the width. We multiply this by two because there are two length values and 2 width values in a rectangle. This gets us P=112 and P=14W. If we divide each side by 14, we get 8. This must be the width, so we multiply by 6. 8 times 6 is 48. Then, we have to multiply both of these by 2. We get 96 and 16. If you add the two, you get 112. Then, simply multiply 96 by 16 to get 1536 in^2.