Question

Please assist me with this problem​

Answer 1

See working below

Explanation:

You can apply Thales Intercept Theorem ("similar triangles")

a.
`(36)/(24)\:=\:(48)/(ET),\:ET\:=\:(24\cdot 48)/(36)\:=\:32`

b.
`(36+24\:)/(AJ)=\:(48+ET)/(40),\:(60\:)/(AJ)=\:(48\:+\:32)/(40),\:(60)/(AJ\:)=\:(80)/(40),\:AJ\:=\:(1)/(2)\left(60\right)\:=\:30`

c.

`\\(48)/(CT)\:=\:(36)/(36+24)\:=\:(27)/(AT),\\\\CT = CE + ET = 48 + 32 = 80\\\\(48)/(80)\:=\:(36)/(60)\:=\:(27)/(AT),\:0.6\:=\:(27)/(AT),\:AT\:=\:(27)/(0.6)\:=\:45`

d.

`(36+24+AJ)/(12\:)=\:(48+ET+40)/(OS)\\\\(36+24+30)/(12)=\:(48+32+40)/(OS),\:(90)/(12)\:=\:(120)/(OS),\:OS\:=\:(12\cdot 120\:)/(90)=\:16`

e.

`(36+24)/(36+24+AJ\:)=\:(48+ET)/(48+ET+40\:)=\:(AT)/(JO)\\\\(60\:)/(36+24+30)=(\:48+32)/(48+32+40)\:=\:(45)/(JO)\\\\(60)/(90)=\:(80)/(120)\:=\:(45)/(JO)\\\\JO\:=\:(135)/(2)\:=\:67.5`

f.

`(36+24+AJ\:)/(36+24+AJ+12)=(\:48+ET+40)/(48+ET+40+OS)\:=\:(JO)/(NS)\\\\(90)/(102)\:=\:(120)/(136)\:=\:(67.5)/(NS)\\\\NS\:=\:(136\cdot 67.5)/(120)=\:76.5`