The length of the hypotenuse of a right triangle is √15 and the length of one leg is 3. What is the length of the other leg?

Answer 1

The Pythagorean Theorem says a² + b² = c² where "a" and "b" are the sides of a right triangle and "c" is the hypotenuse (the side opposite the right angle).

So 3² + x² = (√15)²

Squaring a square root just "undoes" the square root (they are inverse operations), so (√15)² = 15

9 + x² = 15

x² = 15 - 9

x² = 6

x = √6

Answer 2

For a right triangle, the Pythagorean Theorem applies, so a²+b²=c² where a and b are the lengths of legs and c is the length of the hypotenuse. So if we substitute the values from the problem, then we have that

3²+b²=√15²

9+b²=15

9+b²-9=15-9

b²=6

b=√6

So the other leg has a length of √6.

(Ordinarily that last step would result in b=±√6, but in this context we would not give a negative length for the leg of a triangle, so we can leave it as shown above).