Question

The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth of the rectangle is 3/2 times that of the side of the square. Find the length of the diagonal of square. 
1. 5√2 cm
2. 20 cm
3. 10√2 cm
4. 10 cm

Answer 1

Correct Answer - Option 3 : 10√2 cm

Given:
Length of the rectangle(l) = 20 cm
Breadth of the rectangle(b) = (3/2) × (Side of the square)
Area of the rectangle = 3 × Area of the square

Concept used:
Area of the rectangle = Length(l) × Breadth(b)
Area of the square = (Side)²
Diagonal of the square = √2 × (side)

Calculation:
Let the side of square be a.
Breadth of the rectangle(b) = (3/2) × (Side of the square) = (3/2) × a
Area of the rectangle = 3 × (a)²
⇒ l × b = 3 × (a)² 
⇒ 20 × (3/2) × a = 3a²
⇒ 10 × 3 = 3a²/a
⇒ 30 = 3a
⇒ a = 10 cm
Diagonal of the square = √2 × a
⇒ √2 × 10
⇒ 10√2
∴ The length of the diagonal of square is 10√2 cm.