Question

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Answer 1

9514 1404 393

Answer:

• width: 4 ft
• length: 13 ft

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.