Question

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. 10
2. 12
3. 14
4. 16

Answer 1

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