Question

Solve for the missing side lenghts. leave answer in simplest radical form *Special Right Triangle*

Answer 1

x=2

Step-by-step explanation

we have 2 triangles (45-45-90 degrees)

for triangle 1

`\begin{gathered} \text{side}=y \\ \text{hypotenuse}=4 \\ \text{then} \\ 4=y\sqrt[]{2} \\ \frac{4}{\sqrt[]{2}}=y=\frac{2\sqrt[]{2}\sqrt[]{2}}{\sqrt[]{2}}=2\sqrt[]{2} \end{gathered}`

now, for triangle 2

side=x

hypotenuse = y

then

`\begin{gathered} \text{hypotenuse}=y=2\sqrt[]{2} \\ \text{the side} \\ \text{hypotenuse}=x\sqrt[]{2} \\ \text{Hence} \\ 2\sqrt[]{2}=x\sqrt[]{2} \\ x=2 \end{gathered}`

I hope this helps you