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Basic Proportionality Theorem

In Δ PQR,MN...

Question

In $Δ P Q R, M N | | Q R$ and given that PM = 3 cm MQ = 8cm, QR = 32 then MN is (image)

A

4 cm

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B

8.7 cm

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C

12 cm

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D

14 cm

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Solution

The correct option is B 8.7 cm
In $Δ P M N a n d Δ P Q R, ∠ P i s c o m m o n, ∠ P M N = ∠ P Q R a n d ∠ P N M = ∠ P R Q [c o r r e s p o n d i n g a n g l e p a i r s]$

Hence the triangles are similar by AAA.

So, $\frac{P M}{P Q} = \frac{M N}{Q R} ⟹ \frac{3}{11} = \frac{M N}{32} ⟹ M N = 8.7$ .

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