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Question
In the figure, given 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.
Solution
i. In ΔACB and ΔFCE, we have
∠ACB = ∠FCE ...(Vertically opposite angles)
∠CBA = ∠CEF ...(Alternate angles)
∴ ΔACB ∼ ΔFCE ...(AA axiom of similarity)
Thus their corresponding sides are proportional.
∴ `(AB)/(BC) = (EF)/(EC)`
`\implies (7.5 cm)/(x cm) = (4.5 cm)/(3 cm)`
`\implies x = ((7.5 xx 3)/4.5) cm`
= `225/45 cm`
= 5 cm
ii. In ΔEBF and ΔCBD, we have
∠B = ∠B ...(Common angle)
∠EFB = ∠CDB ...(Corresponding angles)
∠BEF = ∠BCD
∴ ΔEBF ∼ ΔCBD ...(AA axiom of similarity)
Thus, `(EB)/(CB) = (EF)/(CD)`
`\implies (EC + CB)/(CB) = (4.5 cm)/(y cm)`
`\implies (3 + x)/x = 4.5/y`
`\implies ((3 + 5) cm)/(5 cm) = 4.5/y`
`\implies y = (4.5 xx 5)/8`
= `45/16 cm`
= `2 13/16 cm`
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