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Solution for 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. - CBSE Class 10 - Mathematics

ConceptCriteria for Similarity of Triangles

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.

Solution

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

∠ACD = ∠AEF                           [corresponding angles]

Then, ΔACD ~ ΔAEF                 [By AA similarity]

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

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

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

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Solution 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. Concept: Criteria for Similarity of Triangles.
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