If two sides of a right angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?

The other side is either 7.81 cm or 3.32 cm.

Step-by-step explanation:

The two sides of a right triangle are 5 cm and 6 cm.

There are three different ways this can happen.

1. 5 cm and 6 cm are the two legs of the 90° angle and hence, the hypotenuse is the third side.

Now, applying Pythagoras Theorem,

Hypotenuse = cm.

2. Then one leg of the right angle is 6 cm and 5 cm is the hypotenuse.

But as 5 < 6, so, this is not possible as the length of the hypotenuse is more than the lengths of the legs.

3. 6 cm is the length of the hypotenuse and one leg is 5 cm.

The applying the Pythagoras Theorem, the length of the other leg will be given by cm. (Answer)

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y