If the perimeter of a rectangle is 10 cm and the area is 4 cm^2

If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is

  1. 6 cm
  2. 5 cm
  3. 4.5 cm
  4. 4 cm

Answer

Perimeter of rectangle = 2(L + B) = 10

L + B = 5

Area of rectangle = L × B = 4

The only option that satisfies both the equations is L=4 and B=1.

L × (5-L) = 4

L2 - 5L + 4 = 0

L2 - L - 4L + 4 = 0

L(L - 1) - 4(L - 1) = 0

(L - 1)(L - 4) = 0

L = 1, 4

So, the length is 4 cm and the breadth is 1 cm.

The correct option is D.