Question

In the figure,AP:PC=3:4,BM:MP=3:2 and BQ=12cm find 4/7×AQ

Answer 1

4/7×AQ. = 8 cm  if ,AP:PC=3:4,BM:MP=3:2 and BQ=12cm

Step-by-step explanation:

Let draw PN ║  QM or QC  (as M lies on QC)

=>  ΔAPN ≈ ΔACQ

AN/QN = AP/PC

=> AN/QN = 3/4

ΔBMQ ≈ ΔBPN

BQ/QN = BM/MP

=> 12/QN = 3/2

=> QN = 8

AN/QN = 3/4

=> AN/8 = 3/4

=> AN = 6

AQ = AN + QN = 6 + 8 = 14

(4/7) * AQ

= (4/7) * 14

= 8 cm

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Answer 2

4/7×AQ=8

Step-by-step explanation:

In triangle ABC, let Q be a point on AB and D be a point on AC.

Construction: Join CQ, draw OD parallel to CQ.  

In triangle BOD,

3x/2x=12/OQ

OQ=8

In triangle AOD,

AO/OQ=3x/4x

AO/8=3/4

AO=6

AO+OQ=8+6

             =14

Now,

4/7×AQ=4/7×14

             =8.