Problem
A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. Find the other leg.
📝Step-by-Step Solution
1
Write the Pythagorean theorem
The Pythagorean theorem states: a² + b² = c², where c is the hypotenuse (longest side).
a² + b² = c²
2
Identify what we know
One leg a = 5, hypotenuse c = 13. We need to find leg b.
a = 5, c = 13, b = ?
3
Substitute into the formula
Plug in the known values: 5² + b² = 13²
5² + b² = 13²
4
Calculate the squares
25 + b² = 169
25 + b² = 169
5
Isolate b²
Subtract 25 from both sides: b² = 169 - 25 = 144
b² = 144
6
Take the square root
b = √144 = 12
b = 12 cm
✅Final Answer
The other leg is 12 cm
This is a 5-12-13 Pythagorean triple! Common Pythagorean triples to memorize: 3-4-5, 5-12-13, 8-15-17, 7-24-25. When finding a leg (not hypotenuse), rearrange to: leg² = hypotenuse² - other leg².
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