Question

A triangle has a leg with a length of 3 and a hypotenuse with a length of 6.What is the length of the other leg?

Answer 1

3
`√(3)`

Explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the length of the other leg, then

x² + 3² = 6², that is

x² + 9 = 36 ( subtract 9 from both sides )

x² = 27 ( take the square root of both sides )

x =
`√(27)` =
`√(9(3))` =
`√(9)` ×
`√(3)` = 3
`√(3)` ← exact value