Question

In ∆ ABC, P and Q are points on sides AB and AC respectively such that, PQ || BC, if AP = 12 cm, PB = 8 cm, AQ = 9 cm, Find AC​

Answer 1

Answer:

AC=15

Step by step explanation:

AP/PB=AQ/QC (BPPT THEOREM)

let QC=x

12/8=9/x

by cross multiplication,

x=6

QC=6

AC=AQ+QC

AC=9+6

so,AC=15

Answer 2

Thales Theorem Statement

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

AP/PB= AQ/QC

put all values

AP = 12 cm, PB = 8 cm, AQ = 9 cm, QC=x

$12 \div 8 = 9 \div x$

$x = 9 \times 8 \div 12$

$x = 6$

QC=6

AC=9+6=15