Question

ABC is a triangle and pQ is a straight line
melting AB in P & AC in Q. If Ap=1cm & BP=3cm
AQ = 1.5cm, CQ= 4.5cm.
Prove that: (ar of AAPQ) = 1/16 (ar of ABC)​

Answer 1

Answer:

SOLUTION :  

Given : In ΔABC, PQ is a line segment intersecting AB at P and AC at Q. AP = 1 cm , PB = 3cm, AQ= 1.5 cm and QC= 4.5cm.

In ∆APQ and ∆ABC,

∠A = ∠A               [Common]

AP/AB = AQ/AC        [Each equal to 1/4]

∆APQ ~ ∆ABC      [By SAS similarity]

We know that the ratio of the two similar triangles is equal to the ratio of the squares of their corresponding sides

ar∆APQ /ar∆ABC = (AP/AB)²

ar∆APQ /ar∆ABC = ( ¼)²

ar∆APQ /ar∆ABC = 1/16

ar∆APQ =  1/16 × ar∆ABC  

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Step-by-step explanation:

Hope we can prove like this