Question

In the given figure ΔACB ~ ΔAPQ, if BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, AP= 2.8 cm, Find CA and AQ.

Answer 1

Answer:

Values of : CA = 5.6cm , AQ = 3.25cm

Step-by-step explanation:

Given : In the fig. triangle ACB is similar to triangle APQ .

             BC =8cm , PQ =4cm , BA =6.5cm and AP =2.8cm.

To Find : Values of CA and AQ.

Steps : Both the triangles are similar.

             So,  their corresponding sides and angles will be equal.

         BC/PQ = BA/AQ = CA/AP

          8/4 = 6.5/AQ = CA/2.8

  To find AQ :    8/4 = 6.5/AQ

                           8AQ = 26

                            AQ = 26/8

                             AQ = 3.25cm

To find CA :   8/4 = CA/2.8

                      4CA = 22.4

                        CA = 22.4/4

                        CA = 5.6cm

Therefore , values of CA = 5.6cm and AQ =3.25cm.

               

Answer 2

Answer:

Given : ΔACB∼ΔAPQ , BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, and AP = 2.8 cm

ΔACB∼ΔAPQ

BA/AQ = CA/AP = BC/PQ

[Since, triangles are similar , hence corresponding sides will be proportional]

Therefore,  6.5/AQ = 8/4

AQ = (6.5x4)/8

AQ = 6.5/2

AQ = 3.25 cm

Similarly,  CA/AP = BC/PQ

CA/2.8 = 8/4

CA = 2.8 x 2

CA = 5.6 cm

Hence, CA = 5.6 cm and AQ = 3.25 cm.

                                             (OR)

Given,

ΔACB ∼ ΔAPQ

BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm

Required to find: CA and AQ

We know that,

ΔACB ∼ ΔAPQ [given]

BA/ AQ = CA/ AP = BC/ PQ [Corresponding Parts of Similar Triangles]

So,  

6.5/ AQ = 8/ 4

AQ = (6.5 x 4)/ 8

AQ = 3.25 cm

Similarly, as

CA/ AP = BC/ PQ

CA/ 2.8 = 8/ 4

CA = 2.8 x 2

CA = 5.6 cm

Hence, CA = 5.6 cm and AQ = 3.25 cm.