If the area of the rectangle is 170 square feet the what is the length and the width

Question

the width of a rectangle is 7 feet less than its length. If the area of the rectangle is 170 square feet the what is the length and the width

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to find a way to relate the quantities of a rectangle to one another. On this one we have

Area = L x W = 170

L = W + 7  because it’s 7 feet longer than it is wide

I would plug the second equation into the first to get

(W + 7)(W) = 170

W^2 + 7W – 170 = 0

(W + 17)(W – 10) = 0

W = -17 or W = 10 , but only W = 10 makes sense in this context since we need a positive value for a dimension

So Width = 10, then Length = W + 7 = 10 + 7 = 17

Meaning that the dimensions here are 10 feet wide by 17 feet long

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

let the width be x

 

then length = x + 7

 

Area= x(x+7) = 170

 

expanding; x^2 + 7x - 170 = 0

 

factorizing (x + 17)(x-10) = 0; (could also have used the quadratic formula)

 

x = -17 or 10; discarding the negative sign as it has no practical significance for this problem

 

x (width) = 10ft; hence the length = x+7 = 17ft

 

check; 10 * 17 = 170 and 17-10 = 7