Question

Darrin is hanging 200 feet of Christmas garland on the fencing around his house. The fence has the shape of a rectangle and fully encloses the house and its front, side and back yards. The length is 5 feet less than 5 times the width.Find the length and width of the fencing. Give the measurements in decimal form.

Answer 1

the width is 17.5 feet and the length is 82.5 feet.

Explanation:

The house has a rectangular shape and we know that the length is 5 feet less than 5 times the width.

We will call the width x, thus, the length would be represented as 5x-5 (5 less than 5 times the width).

Since Darrin is going to hang garland around the perimeter of the house, we know that the perimeter is 2 times the length plus two times the width and this equals 200.

Let's write this in algebraic form

`width = x\\length= 5x-5\\Perimeter= 2width +2length=200\\200=2(x)+2(5x-5)\\200=2x+10x-10\\200=12x-10\\200+10=12x\\210=12x\\210/12=x\\x=17.5`

Therefore, the width is 17.5 feet.

Now, the length is 5x-5, thus substituting the 17.5 in this equation we have:

`5x-5=5(17.5)-5=87.5-5=82.5` feet

Therefore, the width is 17.5 feet and the length is 82.5 feet.