Question

Given that

a= 6 m, work out x
Give your answer as an exact surd in its simplest form.

Diagrams are not to scale

Answer 1

`x=3√(2)`

Explanation:

In a right triangle, the "hypotenuse" is the side opposite of the 90 degree angle. That side is "a"

Using pythagorean theorem, we can write:

Leg^2 + Leg^2 = Hypotenuse^2

Note: legs are the other 2 sides, x and x respectively

Now we can write:

`x^2 + x^2 = a^2`

a is 6 meters, so replacing a with 6 and solving we get:

`x^2 + x^2 = a^2\\2x^2=6^2\\2x^2=36\\x^2=18\\x=√(18)`

To simplify the surd, we can use the property shown below:

`√(x*y)=√(x)  √(y)`

Also

`√(x) √(x) =x`

Now simplifying:

`x=√(18) \\x=√(9*2)\\ x=√(9) √(2) \\x=3√(2)`