Question

For problems 22 through 24, find the value of x.

Answer 1

All of your shapes are formed like this: pick a triangle, and connect the middle points of two sides. In all those cases, you have that the inner triangle is similar to the whole triangle, with scale factor 1/2.

Look at the attached picture. ABC is similar to CDE, and since the correspondent sides are one the double of the other (AC=2DC and BC=2CE), we deduce that AB=2DE.

So, in your exercises, you'll always have to setup this equation: the inner segment is half of the base. For example, in the first exercise, you have

`x-4=(17)/(2) \iff 2x-8=17 \iff 2x=25 \iff x=12.5`

Work similarly for the second and third triangle and you'll be done

Answer 2

see explanation

Explanation:

The segment bisecting 2 sides of the triangles are midsegments and are all one half the measure of the third side.

22

x - 4 = 0.5 × 17 = 8.5 ( add 4 to both sides )

x = 12.5

23

x + 2 = 0.5 × 38 = 19 ( subtract 2 from both sides )

x = 17

24

5x - 4 = 2 × 8 = 16 ( add 4 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4