Question

Show how to answer thanks

A rectangle has a length that is 1 more than three times the width the area is 52 square feet. find the length and the width

Answer 1

9514 1404 393

Answer:

• width: 4 ft
• length: 13 ft

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.