The perimeter and the area of a rectangular sheet are 42 m and 108 m² , respectively. The length of the diagonal is:

15 m

We know that,

Area of rectangle = length × breadth = 108

Perimeterof rectangle = 2(length + breadth)

We have,

The perimeter = 42 m

Area of rectangle =  108 m²

According to the question,

2(length + breadth) = 42 m

Length + Breadth = 21 m

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

So, Area = 108

(a) × (21-a) = 108

= 21a - a² = 108

Solving equation we get

a = 12, 9

Length = 12 m

Breadth = 21 - 12 = 9 

Diagonal = √(length² + breadth²)

= √(12² + 9²) = √(144 + 81)

= √225  = 15