Question

in the figure, AB||CD||EF. If AB = 6cm, CD = xcm, EF = 10cm, BD = 4cm and DE = y cm, calculate the values of x and y. ​

Answer 1

$\mathcal {\orange{SOL:-</p><p>}}$

AB || CD || EF

In △ ABD and △RED

∠ABD = ∠RED .... Alternate angle

∠BAD = ∠DRE ...... Alternate angle

•°• △ ABD ~ △RED . ...AA test of similaritie

•°• AB/RE = BD/ED ...c.s.s.t

•°• 6/10 = 4/y

•°• 40/6 = y

•°• 6.66 = y

$\tt \red{now,}$

In △ABE and △CDE

∠ABE = ∠CDE .......corresponding angle

∠BEA = ∠DEC .......vertically opposite

•°• △ABE ~ △CDE ...by AA test of similaritie

•°• AB/CD = BE/DE ....c.s.s.t

•°• 6/x = (BD + DE)/6.66

•°• 6/x = 10.66/6.66

•°• 39.96/10.66 = x

•°• 3.74 = x

The value for x and y is 3.74 and 6.66.

Answer 2

Answer:

The value of x = 3.74

The value of y = 6.66