Mathematics: Given that a= 6 m, work out x give your answer as an exact surd in its simplest form. diagrams are not to scale

C im pretty sure, could be wrong.Step-by-step explanation:...

Given that a= 6 m, work out x give your answer as

charlettethomap7e9st

09.01.2022

$x=3\sqrt{2}$

Step-by-step 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:

$x^2 + x^2 = a^2\\2x^2=6^2\\2x^2=36\\x^2=18\\x=\sqrt{18}$

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

$\sqrt{x*y}=\sqrt{x} \sqrt{y}$

Also

$\sqrt{x} \sqrt{x} =x$

Now simplifying:

$x=\sqrt{18} \\x=\sqrt{9*2}\\ x=\sqrt{9} \sqrt{2} \\x=3\sqrt{2}$

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