Investigate the Relationship of the Sides of a Right-Angled Triangle

A long, long, long, long.....very long time ago a mathematician and his students found a relationship between the sides of a right-angled triangle!

 

You will need some paper, a ruler and a calculator for this activity!

 

Step 1

Draw a triangle in the middle of the paper. The base needs to be 3 cm and the height 4 cm.

Draw it to scale as accurately as you can and join the two lines together to form a triangle.

 

 

Step 2

Draw an exact square from each of the two sides.

One should be 3 cm x 3 cm and the other 4 cm x 4 cm.

 

 

The area of those squares will be 9 cm² and 16 cm²

 

Step 3

Measure the diagonal.

Did you get 5 cm?

 

 

Now draw a square on the diagonal side 5 cm x 5 cm

The area of that square is 5 x 5 = 25 cm²

 

Step 4

Do you notice anything about the area of the three squares?

 

16 cm² + 9 cm² = 25 cm²

 

That means, if we add the areas of the two shorter sides together they fit exactly into the square of the diagonal side.

 

We call the diagonal side, opposite the right angle the hypotenuse. 
 

 

If we know the two shorter sides we can work out the area on the hypotenuse!

 

Let's try some!