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

Answer:

3$\sqrt{3}$

Step-by-step 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 = $\sqrt{27}$ = $\sqrt{9(3)}$ = $\sqrt{9}$ × $\sqrt{3}$ = 3$\sqrt{3}$ ← exact value