A rectangle has a perimeter of 22 inches and an area of 24 square inches which of the following could be its dimensions?

A. 4in and 6in

B. 7in and 4in

C. 2in and 11in

D. 3in and 8in

The answer is D.) 3 inches & 8 inches

a=lw

a=3*8

a=24

p=2 (l+w)

p=2 (3+8)

p=2 (11)

p=22

Let x represent the length and w represent the width of the rectangle.

Perimeter of the rectangle is twice the sum of its length and width. So we can write:

Perimeter = 2 (Length + Width)

22 = 2 (x + y)

11 = x + y (1st Equation)

Area of a rectangle is the product of its Length and Width. So we can write:

Area = Length x Width

24 = xy (2nd Equation)

From 1stequation, we can write: x = 11 - y

Using this value of x in 2nd Equation, we get:

24=y (11-y)

24 = 11y - y²

y² - 11y + 24 = 0

y² - 3y - 8y + 24 = 0

y (y-3) - 8 (y-3) = 0

(y - 3) (y - 8) = 0

⇒ y = 3, y = 8

Since x = 11 - y,

For y = 3, x = 11 - 3 = 8

For y = 8, x = 11 - 8 = 3

So, the dimensions of the rectangle will be 8 in and 3 in.

Thus, option D gives the correct answer