Question

CAN SOMEONE HELP ME PLS?

Answer 1

x = 8

`\overline{AC}` = 30

`\overline{CD}` = 10

Explanation:

Triangle
`\triangle ABC` and triangle
`\triangle DEC` are similar because they have 2 congruent angles. We can find the scale factor between them by comparing the length of
`\overline{BC}` and
`\overline{EC}` in a fraction, resulting in us finding the scale is 3:1 from
`\triangle ABC` to
`\triangle DEC`.

Now we can solve for x using a proportion.

`(3)/(1) = (x+22)/(x+2)` | Cross multiply

3x+6 = x+22 | Subtract x from both sides

2x+6 = 22 | Subtract 6 from both sides

2x = 16 | Divide both sides by 2

x = 8

Now we can solve for
`\overline{AC}` and
`\overline{CD}` by substitution.

`\overline{AC}` = x + 22 = 8 + 22 = 30

`\overline{CD}` = x + 2 = 8 + 2 = 10

These are your answers

- Kan Academy Advance