A yard has a perimeter of 216feet. If 10times the length of the yard equals 17 times the​ width, what are its​ dimensions

Answer 1

Question: A yard has a perimeter of 216feet. If 10times the length of the yard equals 17 times the​ width, what are its​ dimensions

Equation: 216 feet = 2l + 2w

In order to solve you'll need one variable. Therefore, solve for either length or width so that the equation can be rewritten with one variable.

10l = 17w

l = 17/10w

Now, rewrite the equation 216 = 2(17/10w) + 2w

216 = (34/10)w + 2w

216 = (34/10)w + (20/10)w

216 = (54/10)w

(216)/(54/10) = w

2160/54 = w

Simplify w and plug it in for w to solve for the length when the perimeter is 216 yards.

216 = 2(l) + 2(w)

216 = 2l + 2(40)

216 - 80 = 2l

136 = 2l

68 = l

Answer: Therefore, the dimensions of the yard are 68 by 40.

Answer 2

Hi, Tonnaysha!

First you need to use the formula for perimeter.

P= 2L+2W

Then translate the statement: 10 times the length equals 17 times the width

10L=17W

Then solve that equation for L.

L=(17/10)W (divided 10 on both sides)

Now you know: P=216 L=17/10W and W=W

Replace P, L, and W into the perimeter formula

P= 2L +2W

216 = 2((17/10)W) + 2W

Now solve for W.

216 = (34/10) W + 2W ———-> 17/5W + 10/5W

216 = 27/5 W ————-> (5/27)216= 27/5W (5/27)

40= W

Plug in W=40 to find L

216= 2L+2(40)

I will let you finish the problem. I hope this helped you get started.

Mrs. S