Question

A rectangle has its length equal to the square of its width. Given that the perimeter of the rectangle is 24, compute the area of the rectangle.

a 12
b 16
c 24
d 27
e NOTA

Answer 1

Define x:

Let the width be x

The length = x²

Form equation and solve for x:

Perimeter = 2 ( Length + Width)

24 = 2 (x + x²)

12 = x + x²

x² + x - 12 = 0

(x - 3) (x + 4) = 0

x = 3 or x = - 4( rejected, since length cannot be negative)

Find the area:

width = x = 3

Length = x² = 3² = 9

Area = Length x Width

Area = 9 x 3 = 27 units ²

Answer: (d) 27 units²