There is a 2.5 meter wide path around the rectangular garden of Shiraj’s. The area of path is 165 sq. meter. Let us calculate the area of garden and the length of diagonal.
Let L and B be the total length and total breadth of the rectangle covering the path and the garden respectively.
Length of the garden
= L - 2 × width of path
= L – 2(2.5) = (L – 5)
Breadth of the garden
= B - 2 × width of path
= B – 5
We know, area of square = length × breadth
Area of the garden = (L - 5)(B - 5)
Total Area = L × B
Area of path = Total Area – Area of garden = 165
LB - (L - 5)(B - 5) = 165
⇒ LB – LB + 5L + 5B - 25
⇒ 5B + 5L - 25 = 165
⇒ 5(L + B) = 190
⇒ L + B = 38m
Let L = 20m
B = 18m
Area of the garden = (20 - 5)(18 - 5) = 195m2
We know, diagonal of a rectangle 
Where, L = length of rectangle and B = breadth of rectangle
Length of the Diagonal = 
= 27m