68.4k views
0 votes
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.

1 Answer

5 votes

Answer:

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.

User Tony Stark
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories