A rectangular room has an area of 60 $$m^{2}$$ and perimeter of 34 m.The length of the diagonal of the rectangular room is same as the side of a square.The area of the square (in $$m^{2}$$)

Let the length and breadth of the rectangular room is $$l\ and\ b$$

Given, 

Area = 60 $$m^2$$

We know, Area = $$l\times\ b$$

i.e, $$l\times\ b\ =\ 60$$

Perimeter = $$2\left(l+b\right)\ $$ = 34 (given)

i.e $$l+b\ =\ 17$$

By solving, we get l = 12 cm and b = 5 cm

Diagonal of a rectangle = $$l^2+b^2\ =\ d^2$$

$$\therefore\ d\ =\ \sqrt{\ 144+25}=13$$

According to question, 

Diagonal of the rectangular room is same as the side of a square

i.e side of square = 13

Area = square = $$\left(side\right)^2$$

= $$\left(13\right)^2$$ = 169

Option A is correct.