Question

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

Answer 1

The answer is 4/7 × AQ = 4/7 × 14 = 8

Step-by-step explanation:

• As we are given ratio of sides therefore we can apply property lines method.

• Now according to figure draw a line to extend P to meet AQ in Z such that

        PZ || CQ

        Therefore AQ = AZ + QZ

         Now, In triangle △PZB,  

         We have, PZ || QM

• Now, by using Basic proportionality theorem

        BM/MP = BQ/QZ

• From the question it is given that the ration between

        BM : MP =  3 :2

        BQ = 12 cm

        Now BM / MP = BQ/QZ

        3/2 = 12/QZ

        QZ = 8cm

        Now, In triangle △AQC,  We have PZ || QC.

• Therefore by applying Basic proportionality theorem

         AZ /QZ = AP/ PC

         AZ /8 = 3/4

         AZ = 3/8 x 4 = 6cm

         Now put the values in AQ = AZ + QZ = 6 + 8 = 14 cm

         Therefore the answer is 4/7 × AQ = 4/7 × 14 = 8