1.

The perimeter of a rectangle is 14 cm and the length of its diagonal is 5 cm. What is its area in sq cm?1. 102. 123. 144. 16

Answer» Correct Answer - Option 2 : 12

Given:

The perimeter of a rectangle = 14 cm

Diagonal = 5 cm

Formula Used:

Perimeter of rectangle = 2(Length + Breadth)

Area of rectangle = Length × Breadth

(Diagonal)2 = (Length)2 + (Breadth)2

Calculation:

Perimeter of rectangle = 2(Length + Breadth)

⇒ 14 = 2(Length + Breadth)

⇒ 7 = (Length + Breadth)      ----(1)

⇒ (5)2 = (Length)2 + (Breadth)2

⇒ 25 = (Length)2 + (Breadth)2      ----(2)

From equation (1) and equation (2)

25 = (Length)2 + (7 - Length)2

⇒ 25 = l2 + 49 - 14 l + l2

⇒ (l - 3)(l - 4) = 0

⇒ l = 3 cm

⇒ l = 4 cm

If length is 3 cm then breadth is 4 cm.

If breadth is 4 cm then the length is 3 cm.

Area of rectangle = Length × Breadth

∴ Area of rectangle = 3 × 4 = 12 cm2

The correct option is 2 i.e. 12 cm2


Discussion

No Comment Found

Related InterviewSolutions