Question

Please help me with this I need the answer squared

Answer 1

We have a right triangle and two of its sides: one leg and the hypotenuse. In order to find the remaining side we can use the pythagorean theorem. For a right triangle with legs a and b and hypotenuse c we have:

`c=\sqrt[]{a^2+b^2}`

Using this in our question we get:

`\begin{gathered} 9=\sqrt[]{5^2+x^2} \\ 9=\sqrt[]{25+x^2} \end{gathered}`

So the equation to be used to find the missing length is:

`9=\sqrt[]{25+x^2}`

In order to find x we can square both sides of that equation:

`\begin{gathered} 9^2=(\sqrt[]{25+x^2})^2 \\ 81=25+x^2 \end{gathered}`

Then we substract 25 from both sides:

`\begin{gathered} 81-25=25+x^2-25 \\ 56=x^2 \end{gathered}`

And we apply a square root to both sides:

`\begin{gathered} √(56)=√(x^2) \\ x=\sqrt[]{56} \end{gathered}`

And that's the value of x.