The area of a rectangle in 60 cm2 and its perimeter is 34 cm, then the length of the diagonal is

Let the length and breadth of rectangle be $$l$$ and $$b$$ cm respectively

=> Diagonal = $$d = \sqrt{l^2+b^2}$$ cm

Area of rectangle = $$lb=60$$ ------------(i)

Perimeter of rectangle = $$2(l+b)=34$$

=> $$l+b=\frac{34}{2}=17$$

Squaring both sides,

=> $$(l+b)^2=(17)^2$$

=> $$l^2+b^2+2lb=289$$

=> $$l^2+b^2+2(60)=289$$     [Using (i)]

=> $$l^2+b^2=289-120=169$$

=> $$\sqrt{l^2+b^2}=\sqrt{169}$$

=> $$d=13$$ cm

=> Ans - (D)