Q1 of 8 Page 56

A 10-metre-long rope is to be cut into two pieces and a square is to be made using each. The difference in the areas enclosed must be square metres. How should it be cut?

Let the larger part of rope be ‘x’ and smaller part be ‘y’.


According to question,


x + y = 10 … (1)


Area of larger square – area of smaller square


⇒


⇒


⇒


⇒


⇒


⇒ 8(x – y) = 1


⇒ 8x – 8y = 1 … (2)


Equating equation (1) and (2)


x + y = 10


8x – 8y = 1


Multiply equation (1) by 8


8x + 8y = 80 … (3)


8x – 8y = 1 … (2)


16x = 81



Put in equation (2)



⇒


⇒


⇒


⇒


⇒


⇒


⇒


∴ The length of the rope to after cutting should be respectively.


More from this chapter

All 8 →
4

Four years ago, Rahim’s age was three times Ramu’s age. After two years, it would just be double. What are their ages now?

 5

If the length of a rectangle is increased by 5 metres and breadth decreased by 3 metres, the area would decrease by 5 square metres. If the length is increased by 3 metres and breadth increased by 2 metres, the area would increase by 50 square metres. What are the length and breadth?

 2

The length of a rectangle is 1 metre more than its breadth. Its area is square metres. What are its length and breadth?

3

The hypotenuse of a right triangle is centimetres and its area are square centimetres. Calculate the lengths of its perpendicular sides.