Question

In a rectangle, the ratio of the length to the width is 5 : 2. The length of the rectangle is 13.875 feet greater than the width. What are the perimeter and the area of the rectangle?

Answer 1

Since the ratio of the length to the width is 5 : 2, let's call the length 5x and the width 2x.
If the length is 13.875 feet longer than the width, then length=13.875+width.

Substituting 5x for length and 2x for width:
5x=13.875+2x
Combine like terms by subtracting 2x from both sides:
3x=13.875 (feet)
Divide both sides by 3:
X=4.625 feet

We can solve for the perimeter even without plugging in x to find the length and width; just use the expressions 5x for length and 2x for width.

Perimeter = length + length + width + width = 5x + 5x + 2x + 2x = 14x = 14 * 4.625 =
64.75 feet

Area = length * width = (5x)(2x) = 10x^2 = 10 * (4.625)^2 = 21.004225 square feet (I solved that by typing it out on here, might wanna recheck with a calculator).

Make sure to include the right units. Hope that helped! :)