A rectangular carpet has an area of $$120m^2$$ and a perimeter of 46 meter. The length of its diagonal is:

Let length of rectangle = $$l$$ m and breadth = $$b$$ m

=> Diagonal of rectangle, $$d=\sqrt{l^2+b^2}$$

=> Area = $$lb=120$$ ---------------(i)

and Perimeter = $$2(l+b)=46$$

=> $$l+b=\frac{46}{2}=23$$

Squaring both sides, we get

=> $$(l+b)^2=(23)^2$$

=> $$l^2+b^2+2lb=529$$

=> $$l^2+b^2+2(120)=529$$     [Using equation (i)]

=> $$l^2+b^2=529-240=289$$

Taking square root on both sides

=> $$\sqrt{l^2+b^2}=\sqrt{289}=17$$

$$\therefore$$ Length of diagonal = $$17$$ m

=> Ans - (D)