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Question
From fig., seg PQ || side BC, AP = x + 3, PB = x – 3, AQ = x + 5, QC = x – 2, then complete the activity to find the value of x.
In ΔPQB, PQ || side BC
`"AP"/"PB" = "AQ"/(["______"])` ...[______]
`(x + 3)/(x - 3) = (x + 5)/(["______"])`
(x + 3) [______] = (x + 5)(x – 3)
x2 + x – [______] = x2 + 2x – 15
x = [______]
Solution
In ΔPQB,
PQ || side BC
`"AP"/"PB" = "AQ"/bb"QC"` ...[Base proportionality theorem]
`(x + 3)/(x - 3)` = `(x + 5)/bb(x - 2)`
(x + 3) (x – 2) = (x + 5)(x – 3)
x2 + x – 6 = x2 + 2x – 15
∴ x – 6 = 2x – 15
∴ 2x – x = 15 – 6
∴ x = 9
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