The idea
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. The hypotenuse is opposite the right angle and is the longest side. The relationship applies to right-angled triangles.
Before you begin: Square numbers, take square roots and identify a right angle.
A right-angled triangle has perpendicular sides of 6 cm and 8 cm. Find its hypotenuse.
Label the side opposite the right angle c. It is the hypotenuse and must be longer than eight centimetres.
Square the two known side lengths before adding.
Take the positive square root because a length is positive.
A mistake to avoid
Do not add the lengths directly or stop at the squared length. If a shorter side is missing, subtract its partner’s square from the hypotenuse’s square.
Your turn.
A right triangle has a 13 cm hypotenuse and a 5 cm shorter side. Find its other shorter side.
Show the solution
The unknown is a shorter side, so subtract before taking the positive square root.