An Exploration in Rectangles

Class 6 Maths · Chapter 8: Playing with Constructions · NCERT Ganita Prakash section 8.4

Learn

Here is a puzzle Sahil found. Take a rectangle ABCD with AB = 7 cm and BC = 4 cm. Point X can slide anywhere along side AD, and point Y anywhere along side BC. Join X and Y.

Guess first: where should X and Y be to make XY as short as possible? And as long as possible? Write your guesses, then test them.

A table keeps track of the tries: distance of X from A, distance of Y from B, and the length XY. You will notice a pattern when the first two numbers are the same.

When AX = BY, XY is level and equal to AB = 7 cm: the shortest it can be. XY is longest when X and Y are at opposite corners (X at A and Y at C, or X at D and Y at B): then XY is a diagonal.

Explore: slide X and Y and watch the length XY.

1. Make XY as short as possible.
2. Find a different position that is just as short.
3. Now make XY as long as possible.

Remember

• XY is shortest (equal to AB) when X and Y are the same distance from A and B.
• XY is longest when it is a diagonal of the rectangle.

Quick check

In the rectangle above, AX = 3 cm and BY = 3 cm. How long is XY?

1. 7 cm
2. 3 cm
3. 4 cm
4. 10 cm

Think about it

Can XY ever be shorter than AB? Explain.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.