Q1 of 62 Page 180

In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC.

If AD = 4x-3, BD = 3x-1, AE = 8x-7 and EC = 5x-3, then find the value of x.


Given DE||BC and AD = 4x—3, BD = 3x—1, AE = 8x—7 and EC = 5x—3

Required: x = ?


Here, DE||BC, ∴ By Thales theorem


∴


⇒


⇒ 20x2—12x—15x + 9 = 24x2—8x—21x + 7


⇒24x2 – 20x2 + 12x + 15x—8x—21x—9 + 7 = 0


⇒ 4x2—2x—2 = 0


⇒ 2(2x2—x—1) = 0


⇒ 2x2—x—1 = 0


⇒ 2x2—2x + x—1 = 0


⇒ 2x(x—1) + 1(x—1) = 0


⇒ (2x + 1)(x—1) = 0


⇒ x = 1 or


∴Values x can have are x = 1 and


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In a ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC.

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E and F are points on the sides PQ and PR respectively, of a Δ PQR. For each of the following cases, verify EF||QR.

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