Question

If the area of a rectangle whose length is 4 units more than twice its width is 96 sq. units. What is the perimeter of the rectangle?

1. 54 units
2. 56 units
3. 47 units
4. 44 units
5. 58 units

Answer 1

Correct Answer - Option 4 : 44 units

Calculations:

Let the width of the rectangle (b) = x unit

∴ Length (l) = (2x + 4) units

According to the question,

Area of the rectangle = l × b

∴ 96 = (2x + 4) × x

⇒ 96 = 2x² + 4x

⇒ 2x² + 4x – 96 = 0

⇒ 2x² – 12x + 16x – 96 = 0

⇒ 2x(x – 6) + 16(x – 6) = 0

⇒ (x – 6) (2x + 16) = 0

∴ x = 6 and x = –8

Since, width cannot be negative.

∴ width = x = 6 units

length = (2x + 4)

⇒2 × 6 + 4 = 16 units

∴ Perimeter of the rectangle = 2(l + b)

⇒ 2 × (16 + 6)

⇒ 44 units

The perimeter of the rectangle is 44 units.