Question

In ΔABC, PQ || BC, P ∈ AB, Q ∈ AC. If 4AP = AB and AQ=4, then AC = .....,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct..
(a) 12
(b) 4
(c) 8
(d) 16

Answer 1

In the attachment I have answered this problem.

Concept:

Thale's theorem:

If a line is drawn parallel to one side

of a triangle then it cuts the other two

sides proportionally.

See the attachment for detailed solution

Answer 2

Answer:

16 cm

Step-by-step explanation:

BY THALES THEORE

$\frac{ap}{pb} = \frac{aq}{qc}$

$\frac{ap}{ab - ap} = \frac{aq}{ac - aq}$

$\frac{ap}{4ap - ap} = \frac{4}{ac - 4}$

$\frac{ap}{3ap} = \frac{4}{ac - 4}$

$ac - 4 = 12$

$ac = 12 + 4$

$ac = 16cm$