Question

The diagonal of a square is \(\sqrt{200}\) cm. If the sides of a rectangle are in the ratio 5 : 2, which is the same as the area of the square, then what is the length of the rectangle?
1. \(\rm \sqrt{250} \ cm\)
2. \(\rm \sqrt{200} \ cm\)
3. \(\rm 2\sqrt{10} \ cm\)
4. \(\rm \sqrt{20} \ cm\)

Answer 1

Correct Answer - Option 1 : \(\rm \sqrt{250} \ cm\)

Given:

Diagonal of square = \(√{200}\) cm 

Ratio of the sides of rectangle = 5 : 2 

Area of rectangle = Area of square 

Formulas used:

Diagonal of square = √2 × Side 

Area of square = (Side)²

Area of rectangle = Length × Breadth 

Calculation:

Diagonal of square = \(√{200}\)

⇒ √2 × Side = 10√2 

⇒ Side = 10 cm 

Let the sides of the rectangle be 5b & 2b respectively.

Area of square = Area of rectangle 

⇒ 10 × 10 = 5b × 2b

⇒ b² = 100/10 = 10 

⇒ b = √10 

∴ The length of rectangle = 5b = 5 × √10 

⇒ √250 cm