Question

GIVING 50 POINTS

Find the missing length indicated. Pls show your work

Answer 1

• 24-9=15

`\\ \sf\longmapsto (20)/(3x-18)=(15)/(9)`

`\\ \sf\longmapsto 300=15(3x-18)`

`\\ \sf\longmapsto 300=45x-270`

`\\ \sf\longmapsto 45x=570`

`\\ \sf\longmapsto x\approx 13`

Answer 2

• from scale factors, big triangle : small triangle

`\dashrightarrow \: { \tt{ (24)/((24 - 9)) = ((3x - 18) + 20)/(20) }} \\ \\\dashrightarrow \: { \tt{20 * 24 = (3x + 2) * 15}} \\ \\ \dashrightarrow \: { \tt{480 = 45x + 30}} \\ \\ \dashrightarrow \: { \tt{45x = 450}} \\ \\ \dashrightarrow \: { \boxed{ \tt{x = 10}}}`

• The missing length:

`= { \tt{3x - 18}} \\ \\ = { \tt{3(10) - 18}} \\ \\ = { \tt{30 - 18}} \\ \\ \dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: missing \: length = 12 \: \: }}}}`