Question

GIVING 50 POINTS

Find the missing length indicated. Pls show your work

Answer 1

• 24-9=15

$\\ \sf\longmapsto \dfrac{20}{3x-18}=\dfrac{15}{9}$

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

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

$\\ \sf\longmapsto 45x=570$

$\\ \sf\longmapsto x\approx 13$

Answer 2

Answer:

• from scale factors, big triangle : small triangle

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

• The missing length:

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