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

Hello, Sabrina!

Let's call the width, w.

Then the length is 1 more than 3 times the width so:

l = 3w + 1

Now, if the area is 52 square feet, then:

A = l x w = 52

(3w + 1) w = 3w² + w = 52

3w² + w - 52 = 0

(3w + 13)(w - 4) = 0

Now, solve for w:

w = -13/3 and w = 4

Since you cannot have a negative length, the only answer is 4.

since the length is 3w + 1 = 13

So,

Width = 4 feet

Length = 13 feet