Question

I'm stuck on this multi-step pythagoren Therorem, I have the answer for the first top triangle which is square root 20 and then i've gotten to the last step to solve for x which is 45=x2 but it asks to factor the largest perfect square which of 45 might be 9? i'm confused

Answer 1

Step 1

Consider the triangle with 2 known sides to find the value of the third side

Using Pythagoras theorem

`\begin{gathered} (3^(rd)side)^2=4^2+2^2 \\ 3^{rd\text{ }}Side\text{ = }\sqrt[]{16\text{ +4}} \\ 3^(rd)Side\text{ = }\sqrt[]{20}=2\sqrt[]{5} \end{gathered}`

Step 2

Use the third known side with the second triangle to find the value of x

`\begin{gathered} x^2=5^2-(2\sqrt[]{5)^2} \\ x=\sqrt[]{25-20} \\ x\text{ =}\sqrt[]{5} \end{gathered}`

x, therefore, = √5 in the simplest radical form