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Please help to find the value of x and explain how to get it in simple terms.

Please help to find the value of x and explain how to get it in simple terms.-example-1
User Mincong
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SOLUTION

From the image above


\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}

Considering the bigger right angle triangle,


(3+x)^2=y^2+45

We can obtain the expression of y from the smaller right angle triangle,

Using pythagora's rule, we have


y^2=6^2+x^2

Then, recall


(3+x)^2=y^2+45

Substite the expression for y², we have


(3+x)^2=6^2+x^2+45

Expand the paranthesis, we have


\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}

subtract 9 from both sides, we have


\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}

Divide both sides by 6, we obtain


\begin{gathered} (6x)/(6)=(72)/(6) \\ \text{Then} \\ x=12 \end{gathered}

Therefore

Answer: x= 12

Please help to find the value of x and explain how to get it in simple terms.-example-1
Please help to find the value of x and explain how to get it in simple terms.-example-2
User Rishabh Rajgarhia
by
9.3k points

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