In the figure below AB, CD and EF are parallel lines. Given AB= 7.5 cm, DC= y cm. EF = 4.5 cm, BC= x cm and CE = 3 cm. Calculate the values of x and y.

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Rajan@2021Guru

Asked: March 25, 20212021-03-25T14:28:43+05:30 2021-03-25T14:28:43+05:30In: ICSE

Find the values of X and Y if in the figure below AB, CD and EF are parallel lines. Given AB= 7.5 cm, DC= y cm. EF = 4.5 cm, BC= x cm and CE = 3 cm.

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MathsMentor · Answer 1 · 2021-03-28T13:27:29+05:30

MathsMentor Guru

Consider △ACB△ACB and △CEF△CEF

Both triangles are similar

∴ABEF=x3∴ABEF=x3

⇒7.54.5=x3⇒7.54.5=x3

x=7.54.5×3x=7.54.5×3

∴x=5∴x=5cm

Consider △BCD△BCD and △BFE△BFE

xy=x+34.5xy=x+34.5

5y=5+34.55y=5+34.5

⇒y=5×4.58⇒y=5×4.58

∴y=4516∴y=4516cm