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Question
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 4x − 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x − 3, find the volume of x.
Solution
We have, DE || BC
Therefore, by basic proportionality theorem,
We have,
`"AD"/"DB"="AE"/"EC"`
`rArr(4x-3)/(3x-1)=(8x-7)/(5x-3)`
⇒ (4x − 3)(5x − 3) = (8x − 7)(3x − 1)
⇒ 4x(5x − 3) − 3(5x − 3) = 8x(3x − 1) − 7(3x − 1)
⇒ 20x2 − 12x − 15x + 9 = 24x2 − 8x − 21x + 7
⇒ 4x2 − 2x − 2 = 0
⇒ 2(2x2 − x − 1)= 0
⇒ 2x2 − x − 1 = 0
⇒ 2x2 − 2x + 1x − 1 = 0
⇒ 2x(x − 1) + 1(x − 1) = 0
⇒ (2x + 1) (x – 1) = 0
⇒ 2x + 1 = 0 or x – 1 = 0
⇒ x = −1/2 or x = 1
x = −1/2 is not possible
∴ x = 1
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