Question

The length of a leg in a 45-45-90 triangle is 12v2.What is the length of the hypotenuse?1224O 6V224V2

Answer 1

STEP1: Draw the triangle.

Since two angles of the triangle are equal hence the two legs of the triagle are equal and the lenght are

`12\sqrt[]{2}`

Using the ratio of one of the legs and the hypotenuse side, we have

`\begin{gathered} 1\colon\sqrt[]{2} \\ 12\sqrt[]{2}\colon(12\sqrt[]{2})\sqrt[]{2} \end{gathered}`

Hence the hypothenuse side becomes

`12\sqrt[]{2}*\sqrt[]{2}=12*\sqrt[]{4}=12*2=24`

The lenght of the hypotenuse side is 24