Question

The perimeter and the area of a rectangular sheet are 42 m and 108 m², respectively. The length of the diagonal is:
1. 12 m
2. 15 m
3. 10 m
4. 14 m

Answer 1

Correct Answer - Option 2 : 15 m

Given:

The perimeter & area of rectangle are 42 m & 108 m²

Calculations: 

Area of rectangle = length × breadth = 108

Perimeterof rectangle = 2(length + breadth) = 42

Length + Breadth = 21 m

Let the length be x & breadth '21-x',

So,

Area = 108

(x) × (21-x) = 108

⇒ 21x - x² = 108

Solving equation we get

x = 12, 9

So

Length = 12 m and breadth = 21 - 12 = 9 

Now 

Diagonal = √(length² + breadth²)

⇒ √(12² + 9²) = √(144 + 81)

⇒ √225 

⇒ 15

The correct choice is option 2.