Question

In the given figure, ∆ACB ∼ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

Answer 1

SOLUTION :

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.

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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.

Step-by-step explanation: