Question

SIMILAR FIGURES USE THE SIMILARITY RELATIONSHIP TO FIND THE INDICATED VALUE.

Answer 1

We are given two similar triangles, that means that their corresponding sides are at the same proportion with each other, that is:

`(ST)/(SZ)=(RT)/(YZ)`

Where:

`\begin{gathered} ST=40 \\ SZ=35 \\ RT=3x-7 \\ YZ=2x+2 \end{gathered}`

Replacing the known values, we get:

`(40)/(35)=(3x-7)/(2x+2)`

Now we will solve for "x". First by simplifying the fraction on the left:

`(8)/(7)=(3x-7)/(2x+2)`

Now we multiply both sides by (2x+2):

`(8(2x+2))/(7)=3x-7`

Now we multiply both sides by 7:

`8(2x+2)=7(3x-7)`

Now we solve the parenthesis:

`16x+16=21x-49`

Now we subtract 21x on both sides:

`16x-21x+16=-49`

Now we subtract 16 on both sides:

`16x-21x=-49-16`

Solving the operations:

`-5x=-65`

Now we divide both sides by -5

`x=-(65)/(-5)=13`

Therefore, the value of x is 13. Now we replace in the equations for the segments, like this:

`\begin{gathered} RT=3x-7 \\ RT=3(13)-7 \\ RT=32 \end{gathered}`

For the other segment:

`\begin{gathered} YZ=2x+2 \\ YZ=2(13)+2 \\ YZ=28 \end{gathered}`