Question

in the below figure PQ|| BC and AP : PB = 1 :2 then the ratio of area of triangle ABC and triangle ABC will be-
(I) 1:2
(II) 1:4
(III)1:9
(IV)4:1

Answer 1

Answer:

can u plz tell the names of triangle properly..triangle ABC by triangle ABC does not actually make any sense

but if the ratio is for tri ABC/ tri APQ= 9:1

AND FOR tri APQ/ tri  ABC= 1:9

Answer 2

Answer:

Option(C)

Step-by-step explanation:

Given, AP/PB = 1/2.

Given, AP = x and PB = 2x.

Then, AB = x + 2x = 3x.

In ΔAPQ and ΔABC,

∠A = ∠A

∠APQ = ∠ABC

∴ ΔAPQ ~ ΔABC

∴ AP/AB = AQ/AC = PQ/BC.

∴ ar(ΔAPQ)/ar(ΔABC) = (AP/AB)²

                                    = (x/3x)²

                                    = (1/3)²

                                    = 1 : 9.

Hope it helps!