Question

The length of a rectangle is 8 inches longer than half of its width.The area of the rectangle is 18 square inches.How many inches wide is the rectangle

Answer 1

The correct answer is 2 inches.

Explanation:

Let l inches and w inches be the length and width of a rectangle respectively.

According to the given problem, l - 8 =
`(w)/(2)`.

Area of the rectangle is given to be, according to the question, 18 square inches.

Thus l × w = 18

⇒ l × (2l - 16) = 18

⇒ 2
`l^(2)` - 16l - 18 = 0

⇒
`l^(2)` - 8l - 9 = 0

⇒ ( l - 9) ( l + 1) = 0

The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.

Width of the rectangle is 2 inches.