Find the Hypotenuse (3-4-5 Triangle)

Grade 8

Problem

A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.

📝Step-by-Step Solution

Identify what we know

We have a right triangle with legs a = 3 and b = 4. We need to find the hypotenuse c.

Write the Pythagorean theorem

The formula is a² + b² = c²

a² + b² = c²

Substitute and calculate

3² + 4² = c² → 9 + 16 = c² → 25 = c²

25 = c²

Solve for c

Take the square root of both sides: c = √25 = 5

c = √25 = 5

✅Final Answer

The hypotenuse is 5 units long

The 3-4-5 triangle is the most famous Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, c that satisfy a² + b² = c². Other common triples include 5-12-13 and 8-15-17.

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Pythagorean Theorem Example

A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. Find the other leg.

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