Question

The area of a rectangle is 300 cm² and the length of its diagonal is 25 cm. The perimeter of the rectangle (in cm) is:
1. 121
2. 70
3. 25
4. 176

Answer 1

Correct Answer - Option 2 : 70

Given:

Area of rectangle = 300 cm²

Diagonal = 25 cm

FORMULA USED:

Area of a rectangle = length × breadth

Perimeter of a rectangle = 2 (length + breadth)

Diagonal = √(length2 + breadth2)

Calculation:

According to question,

⇒ length × breadth = 300    

Again,

Diagonal = √(length2 + breadth2)

⇒ √(length2 + breadth2) = 25 

⇒ (length2 + breadth2) = 625

Let the length be a and breadth be b

Then,

⇒ (a + b)² = a² + b² + 2ab

⇒ (a + b)² = 625 + 2 × 300

⇒  (a + b)² = 1225

⇒ a + b = 35

Perimeter of rectangle = 2(a + b)

⇒ 2 × 25

⇒ 50

∴ Perimeter of rectangle is 50.