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In the given figure $△ A B R ~ Δ P Q R,$ if $P Q = 30 cm, A R = 45 cm, A P = 72 cm$ and $Q R = 42 cm$ then PR and BR are cm and cm.

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Detailed Solution

In the given figure

△ A B R ~ Δ P Q R,

P Q = 30 cm, A R = 45 cm, A P = 72 cm

and

Q R = 42 cm

then PR and BR are 27 cm and 70 cm.
Given that ∆ABR~ΔPQR and PQ=30 cm, AR=45 cm, AP= 72 cm, QR=42 cm.
Question Image

The side PR can be represented as PR=AP-AR.
Therefore,

P R = A P − A R ⇒ P R = 72 − 45 ⇒ P R = 27 cm

Δ A B R ~ Δ P Q R

\frac{BR}{AR} = \frac{QR}{PR}

Therefore,

B R Q R = A R P R ⇒ B R 42 = 4527 ⇒ B R = 454227

Further, solve the above rational equation,

B R = 189027 ⇒ B R = 70 cm

The values of PR and BR are 27 cm and 70 cm respectively.

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