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In the given figure ΔACB∿∆APQ, if $B C = 8 cm, P Q = 4 cm, B A = 6.5 cm, AP = 2.8 cm,$ Then CA and AQ are and cm.

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Detailed Solution

In the given figure ΔACB∿∆APQ, if

B C = 8 cm, P Q = 4 cm, B A = 6.5 cm, AP = 2.8 cm,

Then CA and AQ is 5.6 and 3.25 cm.
Given figure is,

Consider the triangles

Δ A B C

and

Δ P Q R

The triangles ACB and APQ are similar.
So sides ratio are equal, or

C A A P = B A A Q = C B Q P

.
Substitute 8 for BC,

4

for PQ, 6.5 for BA, and 2.8 for AP in the equation

C A A P = B A A Q = C B Q P

to find the value of AQ and CA,

C A 2.8 = 6.5 A Q = 84 ⇒ C A 2.8 = 6.5 A Q = 2

C A 2.8 = 2

.
So, the value of

C A = 5.6

cm.
If

6.5 A Q = 2

.
So, the value of

A Q = 3.25

cm.
The value of the CA and AQ is

5.6

cm.and.

3.25

cm respectively.

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