Question

The perimeter of a rectangle is equal to the perimeter of a square whose diagonal is 17√2 m. If the difference between the length and breadth of a rectangle is 10 m, then what is the area of the rectangle?
1. 289 m²
2. 132 m²
3. 264 m²
4. 578 m²

Answer 1

Correct Answer - Option 3 : 264 m²

Given:

The perimeter of a rectangle  = the perimeter of a square

Diagonal of square = 17√2 m

The difference between length and breadth of rectangle = 10 m

Formulae required:

Diagonal of a square = √2 × side 

The perimeter of a square = 4 × side 

The perimeter of a Rectangle = 2 (Length + Breadth)

Calculations:

√2 × side = 17√2

Side = 17 m

Perimeter of a square = 4 × 17 = 68 m

The perimeter of rectangle = 68

2 (length + breadth) = 68

Length + Breadth = 34

⇒ Length + (Length - 10) = 34

⇒ 2 × Length = 34 + 10 

⇒ Length = 44/2 = 22 m

Length = Breadth + 10

⇒ 22 = Breadth + 10

⇒ Breadth = 22 - 10 = 12 m

The area of a rectangle = length × breadth 

⇒ 12 × 22 = 164 m²

∴ The area of a rectangle is 264 m2