the width of a rectangle is 7 feet less than its length. if the area of the rectangle is 170 square feet then 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 then 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 the given 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

l=length

l-7=width

A=l*w

170=l*(l-7)

170=l^2-7l

l^2-7l-170=0

factor

170=17*2*5=17*10 and 17-10=7

(l-17)(l+10)=0

l-17=0

l=17 feet

w=17-7=10 feet