Math, asked by patkarirekha, 10 months ago

In the given figure , AB || CD || EF given AB = 7.5 cm , DC =y cm , EF = 4.5 cm , BC = x cm . Calculate the values of x and y. .​

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Answered by Anonymous
33

\huge\mathbb{SOLUTION:-}

According \:to

Thales\: theorem

∆CDC ∼ ∆ABE

 \frac{cd}{ab}  =  \frac{de}{be}

 \frac{y}{7.5}  =  \frac{de}{be}

1 -  \frac{y}{7.5}  = 1 -  \frac{de}{be}

 \frac{7.5 - y}{7.5}  =  \frac{be - de}{be}

 \frac{7.5 - y}{7.5}  =  \frac{bd}{be} ...... \: (1)

Similarly ∆BDC ∼ ∆BEF

 \frac{bd}{be}  =  \frac{cd}{ef}  =  \frac{bc}{bc + cf}

 \frac{bd}{be}  =  \frac{y}{4.5}  =  \frac{x}{x + 3}  \: ....... \: (2)

From ( 1 ) and ( 2 )

 \frac{7.5 - y}{7.5}  =  \frac{y}{4.5}

7.5y=(7.5)(4.5)-4.5y

12y=(7.5)(4.5)=33.75

y =  \frac{33.75}{12}  = 2.8125

From ( 2 )

 \frac{y}{4.5}  =  \frac{x}{x + 3}

 \frac{2.8}{4.5}  =  \frac{x}{x + 3}

 4.5 x = (2.8) x + 8.4

  4.5 x - 2.8 x = 8.4

1.7 x = 8.4

x=\frac{8.4}{1.7}

\huge\pink{5\:(appr)}

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