Question

Find ALL the missing side lengths. Giveanswers in simplest radical form if necessary.Showing ALL appropriate work.

Answer 1

The two legs of the triangle are equal as shown by the two small lines on the sides.

We can say that each leg of the triangle is equal to "x".

The hypotenuse is "12".

The pythagorean theorem tells us:

`\text{Leg}^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2`

Putting our information, we have:

`x^2+x^2=12^2`

Let's solve for x:

`\begin{gathered} x^2+x^2=12^2 \\ 2x^2=144 \\ x^2=(144)/(2) \\ x^2=72 \\ x=\sqrt[]{72} \\ x=\sqrt[]{36}\sqrt[]{2} \\ x=6\sqrt[]{2} \end{gathered}`

Each side length is equal to

`6\sqrt[]{2}\text{ cm}`