Question

What's AE and AG? (In centimeters)

Answer 1

AE = 26 cm and AG = 32.5 cm

Explanation:

Given

AB = 12 cm

BD = 12 cm

FD = 6 cm

AC = 12 cm

AD = AB + BD =
`12+12=24 \ cm`

Also segment BC is parallel segment ED which is parallel to segment GF

Now by midpoint theorem we can say that

`(AB)/(BD)=(AC)/(EC)\\(12)/(12)=(13)/(EC)\\1 =(13)/(EC)\\EC= 13\ cm`

Now AE = AC + EC =
`13+13=26\ cm`

Also

`(AD)/(FD)=(AE)/(EG)`

`(24)/(6)=(26)/(EG)\\4=(26)/(EG)\\EG=(26)/(4)\\EG=6.5\ cm`

Now AG = AE + EG =
`26+6.5=32.5\ cm`