The length of a rectangle is one greater than three times its width. If the perimeter of the rectangle is 26 feet, what is the area of the rectangle?

The length of a rectangle is one greater than three times its width. If the perimeter of the rectangle is 26 feet, what is the area of the rectangle?
A . 13 ft 2
B . 24 ft 2
C . 30 ft 2
D . 78 ft 2
E . 100 ft 2

Answer: C

Explanation:

The perimeter of a rectangle is equal to 2 l + 2 w , where l is the length of the rectangle and w is the width of the rectangle. If the length is one greater than three times the width, then set the width equal to x and set the length equal to 3 x + 1:

2 × (3 x + 1) + 2 x = 26

6 x + 2 + 2 x = 26

8 x = 24

x = 3

The width of the rectangle is 3 ft and the length of the rectangle is 10 ft. The area of a rectangle is equal to lw ; 10 ft × 3 ft = 30 ft 2 .