MATHS WEEK is under way and, as is our annual tradition, we’re setting our readers some puzzles every night. Give them a go! You can check out other events being held over the next couple of days here.

The Square on the Hippopotamus

While many will remember the name Pythagoras from school, many will not remember his theorem. If you build a square on each side of a right-angled triangle, the area of the two smaller squares added together will equal the area of the largest square.

We can express this in an equation a2 + b2 = c2

Whole numbers that fit this relationship are called Pythagorean Triples.

The smallest triple is 3,4,5. And, you can check this: 32 + 42 = 52

The theorem also tells us that if a triangle obeys this relationship that triangle has a right angle.

Pythagoras was a Greek mathematician and philosopher who lived around 2,500 years ago.

However, Pythagorean triples have been found on Babylonian tablets almost 4,000 years old. While the Babylonians realised the connection to right-angles it is not clear if they had a proof of the theorem.

1) Measuring out right angles is extremely important in construction. Can you figure out how to mark out a right angle using a length of rope?

2) If you walked east 500m and then walked north 1,200m, how far would you be from your starting point?

3) The size of a TV screen is given by the length of the diagonal. A rectangular television screen measures 30 inches diagonally. Its width is 24 inches. What is the height?

***

Thursday’s puzzle: the answers

1) 625m² — A square measuring 25 m × 25 m gives the largest rectangular area.

2) 795.77m² — A circle encloses the largest possible area using 100m of fencing.

3) 48 m² — The lawn measures 8 m × 6 m, after allowing for the 1m path around the inside edge.

4) 6m² (3m x 2m)

5) 123 m² (We can calculate it by starting with a 12 m × 12 m square (144m²) and subtracting the two missing rectangles: 3 x 3 = 9m² and 3 x 4 = 12m².)