The area of a rectangle is 1200 sq cm and its perimeter 140 cm. What is the length of its diagonal?

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

Perimeter of rectangle = $$2(l+b)=140$$

=> $$(l+b)=\frac{140}{2}=70$$

=> $$l=70-b$$ -----------(i)

Area = $$l \times b=1200$$

Substituting value of $$l$$ from equation (i)

=> $$(70-b)b = 1200$$

=> $$b^2-70b+1200=0$$

=> $$b^2-40b-30b+1200=0$$

=> $$b(b-40)-30(b-40)=0$$

=> $$(b-40)(b-30)=0$$

=> $$b=30,40$$

Thus, the length $$l=40$$ cm and breadth $$b=30$$cm

$$\therefore$$ Diagonal of rectangle = $$\sqrt{l^2+b^2}$$

= $$\sqrt{(40)^2+(30)^2} = \sqrt{1600 + 900}$$

= $$\sqrt{2500} = 50$$ cm

=> Ans - (A)