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
