9514 1404 393
Answer:
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is 3w+1 and the area is ...
w(3w+1) = 52
3w² +w -52 = 0
To factor this equation, we need factors of 3·52 = 156 that have a difference of 1. These values are 12 and 13, so we can rewrite the equation as ...
3w² +13w -12w -52 = 0
w(3w +13) -4(3w +13) = 0
(w -4)(3w +13) = 0
The positive value of w that makes a factor zero is ...
w = 4
Then the length is 3w+1 = 3(4) +1 = 13.
The length is 13 ft; the width is 4 ft.
