Question

In Fig below we have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm, calculate the values of x and y.

Answer 1

We have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm

In ΔECD and ΔEAB

∠CED = ∠AEB                         [common]

∠ECD = ∠EAB                          [corresponding angles]

Then, ΔECD ~ ΔEAB            ….(i) [By AA similarity]

`therefore"EC"/"EA"="CD"/"AB"`                  [Corresponding parts of similar Δ are proportional]

`rArr"EC"/"EA"=x/6`                .........(ii)

In ΔACD and ΔAEF

∠CAD = ∠EAF                           [common]

∠ACD = ∠AEF                           [corresponding angles]

Then, ΔACD ~ ΔAEF                 [By AA similarity]

`therefore"AC"/"AE"="CD"/"EF"`

`rArr"AC"/"AE"=x/10`             ..........(iii)

Add equations (iii) & (ii)

`therefore"EC"/"EA"+"AC"/"AE"=x/6+x/10`

`rArr"AE"/"AE"=(5x+3x)/30`

`rArr1=(8x)/30`

`rArrx=30/8=3.75` cm

From (i) "DC"/"AB"="ED"/"BE"

`rArr3.75/6=y/(y+4)`

⇒ 6y = 3.75y + 15

⇒ 2.25y = 15

`rArry=15/2.25=6.67` cm