Question

For what value of x is PQ || BC?
A 5
B. 6
C. 7
D. 8

Answer 1

C. 7

Explanation:

`In\: \triangle ABC\\</p><p>\overline{PQ} \parallel \overline {BC}.. (given) \\`

Therefore, by Basic Proportionality theorem:

`(AP)/(PB) = (AQ)/(QC) \\\\</p><p>\therefore (x)/(x+7) = (x-3)/(x+1) \\\\</p><p> \therefore \: (x - x - 7)/(x + 7) = (x - 3 - x - 1)/(x + 1) \\ (by \: dividendo) \\ \\ ( - 7)/(x + 7) = ( - 4)/(x + 1) \\ \\ (7)/(x + 7) = (4)/(x + 1) \\ \\ 7x + 7 = 4x + 28 \\ \\ 7x - 4x = 28 - 7 \\ \\ 3x = 21 \\ \\ x = (21)/(3) \\ \\ \huge \red{ \boxed{ x = 7}}`