In ΔABC, P and Q are points on AB and BC, respectively, such that PQ || AC. Given that AB = 26, PQ = 7 and AC = 10 find the value of AP.

7.1 7.8 18.2 16.4

7.8

In ΔACB and ΔPCQ ⇒ \(\frac{AC}{CP}\) = \(\frac{AB}{PQ}\) ⇒ \(\frac{26}{CP}\) = \(\frac{10}{7}\) ⇒ CP = 26 x 0.7 = 18.2 As from figure, ⇒ AB = BP + PA ⇒ 26 = 18.2 + AP ⇒ AP = 26 - 18.2 = 7.8 cm Therefore, AP is 7.8 cm.