Question

If the length of one leg of a right triangle is 3 and the hypotenuse is
`√(34)`, what is the length of the other leg?

Answer 1

5

Explanation:

Use the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

We have

`leg=3,\ hypotenuse=√(34)`

Let's mark the other leg as x.

Substitute:

`3^2+x^2=(√(34))^2` use (√a)² = a

`9+x^2=34` subtract 9 from both sides

`x^2=25\to x=√(25)\\\\x=5`

Answer 2

`\huge{\boxed{5}}`

The Pythagorean theorum states that when
`a` and
`b` are sides and
`c` is the hypotenuse,
`a^2 + b^2 = c^2`

So, let's plug in the values.
`3^2 + b^2 = (√(34))^2`

Simplify. The square of a square root is the number inside the square root.
`9 + b^2 = 34`

Subtract 9 from both sides.
`b^2 = 25`

Get the square root of both sides.
`√(b^2) = √(25)`

`b=\boxed{5}`