Question

One side of a rectangle is 11 feet shorter than five times another side. Find the length of the shorter side if we also know that the perimeter of the rectangle is 182 feet

Answer 1

The length of the shorter side of the rectangle is 74 feet.

Let's denote the length of one side of the rectangle as x and the length of the other side as y. According to the given information, one side is 11 feet shorter than five times the other side, which can be expressed as x=5y−11. The perimeter of a rectangle is given by the formula P=2(x+y).

Substitute the expression for x into the perimeter formula:

182=2((5y−11)+y)

Combine like terms and solve for y:

182=2(6y−11)

182=12y−22

12y=204

y=17

Now that we have the value for y, we can find x using the relationship

x=5y−11:

x=5(17)−11

x=85−11

x=74

Therefore, the length of the shorter side of the rectangle is 74 feet.