Question 638925
The formula for finding the perimeter of a rectangle is P = 2L + 2W, where P is your perimeter, L is the length and W is the width.

The question says the Length exceeds the 5 times the width by a foot.  In other words, Length = 5W + 1.  We also know the perimeter is 170 feet, so 2L + 2W = 170.  To solve, replace the L in the last sentence, for 5W + 1:

2(5W + 1) + 2W = 170

Using the distributive property, multiply 2 by what is in the parenthesis:

2(5W + 1) = 10W + 2

So now, our equation is:

10W + 2 + 2W = 170

Combine the like terms on the left side of the equal sign.  This results in

12W + 2 = 170

Now subtract 2 from both sides of the equal sign:

12W + 2 - 2 = 170 - 2

This results in 

12W = 168

Divide both sides of our equation by 12, that way we get W by itself

12W/12 = 168/12

This results in our width:  W = 14 feet

Now, just replace the W with 14 in L = 5W + 1:

L = 5(14) + 1 = 71

Therefore, our length is 71 feet and our width is 14 feet.  To verify, multiply 71 by 2 and 14 by 2 and add those results together.  If they equal 170, our answer is correct:  2 x 71 = 142 and 2 x 14 = 28.  142 + 28 = 170, so our answer is correct.

Final Answer:  Length = 71 feet and Width = 14 feet