Finding the Hypotenuse
Grade 4The theorem
In any right-angled triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides.
a² + b² = c²
Here c is always the hypotenuse — the side opposite the 90° angle. a and b are the two shorter sides.
Finding c
To find the hypotenuse: square both shorter sides, add them, then take the square root. Simple chain.
Always identify the hypotenuse first. It is the side opposite the right angle, not necessarily the one you are solving for in every question.
Worked example
EXAMPLE
A right-angled triangle has shorter sides of 6 cm and 8 cm. Find the hypotenuse.
c² = 6² + 8² = 36 + 64 = 100. c = √100 = 10 cm.
Watch for Pythagorean triples
Some combinations give whole-number answers — these are called Pythagorean triples. Common ones: 3-4-5, 5-12-13, 8-15-17. Spotting them saves calculation time in exams.
