In fig. 4.144, 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.

Question

In fig. 4.144, 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.

Philoid · Accepted Answer

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

In ΔECD and ΔEAB

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

SO, (Corresponding parts of similar triangle are proportion)

Or ………………(ii)

In ΔACD and ΔAEF

Then, ΔACD ~ ΔAEF (By AA similarity)

SO,

Or, …………………….. (iii)

Adding equation iii & ii

So,

Or,

Or, 1 =

Or, x =

Or, x = 3.75cm

From (i) =

Or, =

Or, 6y = 3.75y +15

Or, 2.25y = 15

Or, y =

Or, y = 6.67cm