Question

If the diagonal of a rectangle is 10 cm and is twice the width, then what would be its area?
1. 25√3 sq cm
2. 10√3 sq cm
3. 12.5√3 sq cm
4. 25 sq cm

Answer 1

Correct Answer - Option 1 : 25√3 sq cm

Given 

The diagonal (d) of the rectangle = 10 cm

Diagonal is twice the breadth

Formula used 

Diagonal² = Length² + Breadth²  

Area of rectangle = Length × Breadth

Calculation 

Length of diagonal = 10 cm

⇒ Length of breadth = 5 cm

Let the length be l

10² = l2 +  5²

⇒ l² = 100 - 25 

⇒ l2 = 75

⇒ l = √75

⇒ l = 5√3 

Area of rectangle = 5 × 5√3 = 25√3 

∴ The required answer is 25√3 sq cm