Question

Christy’s plan for a rectangular dog pen is too small. The perimeter needs to be more than 118 feet. If the width should be nine feet shorter than the length, what should the length be?

Answer 1

In a rectangle, opposite sides are equal. Since the perimeter is the sum of all the sides, you can say that for a rectangle that is x by y:
Perimeter = x + x + y + y = 2x + 2y

If x is the width and y is the length, given the constraint "width should be nine feet shorter than the length", we can say that x = y - 9.

Now we can get rid of x and deal only in y's.

Perimeter = 2x + 2y
We know what x is in this case, it's y - 9.

Perimeter = 2(y - 9) + 2y

If we want a perimeter equal to 118, then:

118 = 2(y - 9) + 2y
118 = 2y - 18 + 2y
118 = 4y - 18
136 = 4y
y = 34

The length should be 34 feet to make the perimeter 118 (keep in mind the question said MORE).

The width x = y - 9 = 34 - 9 = 25

Checking our answer, 25 + 25 + 34 + 34 does indeed = 118 so we're good.