Question

Solve for x. Write the reasons next to each step.Submit603x+10US

Answer 1

We can draw the following picture:

From the figure, we can see that triangles ABC and EDC are similar.

Reasons:

By means of AAA (angle-angle-angle) theorem those triangles are similar, that is

they both triangles have the same angles (red, blue, green).

Since both triangles are similar the following ratio must be preserved:

`(60)/(2y)=(3x+10)/(y)`

Now, from this ratio, we must find x.

If we move 2y to the right hand side, we get

`60=2y((3x+10)/(y))`

so we can eliminate y in both, the denominator and numerator. Then, we obtain

`60=2(3x+10)`

which is equal to

`60=6x+20`

If we move 20 to the left hand side as -20, we get

`\begin{gathered} 60-20=6x \\ 40=6x \end{gathered}`

then, we have

`\begin{gathered} x=(40)/(6) \\ x=(20)/(3) \end{gathered}`

Therefore, x is equal to 20/3.