Question

PLEASE HELP ME!!! and please show me how u arrived to ur answer!!

Answer 1

We have two similar triangles in this figures.

We know similar figures have proportional sides.

Let's draw the two triangles separately along with the lengths of their sides.

From the figure, you can see the corresponding sides.

"x - 2 " corresponds with "2x - 2", and

"x + 1 " corresponds with "2x + 5"

Now, we can set up the ratio:

`(x-2)/(2x-2)=(x+1)/(2x+5)`

Now, we cross multiply, do a little algebra, and solve for "x". The process is shown below:

`\begin{gathered} (x-2)/(2x-2)=(x+1)/(2x+5) \\ (x-2)(2x+5)=(2x-2)(x+1) \\ 2x^2+5x-4x-10=2x^2+2x-2x-2 \\ 2x^2+x-10=2x^2-2 \\ x-10=-2 \\ x=-2+10 \\ x=8 \end{gathered}`