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.

Answer 1

Step-by-step explanation:

hope it helps you good afternoon

Answer 2

x = 3.75 cm

y = 6.67 cm

Step-by-step explanation:

Given: AB||CD||EF

AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm

To find: x and y

Solution:

∠CED = ∠AEB (common)

∠ECD = ∠EAB (corresponding angles)

ΔECD ~  ΔEAB (by AA similarity) --- (1)

So EC/EA = CD/AB (corresponding sides)

EC/EA = x/6 ------------(2)

In ΔACD and ΔAEF

∠CAD = ∠EAF (common)

∠ACD = ∠AEF (corresponding angles)

ΔACD ~  ΔAEF (AA similarity)

So AC/AE = CD/ EF

AC/AE = x/10 ------------(3)

Adding 2 & 3, we get:

EC/EA + AC/AE = x/6 + x/10

AE/AE = (5x + 3x)/ 30

1 = 8x/30

x = 30/8 = 3.75 cm

From (1), we know:

DC/AB = ED/BE

3.75/6 = y/(y+4)

6y = 3.75y + 15

2.25y = 15

y = 15/2.25 = 6.67 cm