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 = [______]

Answer 1

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