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In the given $Δ P Q R,$ LM is parallel to QR and $P M : M R = 3 : 4$ . Calculate the value of $a r (Δ LMN) a r (Δ MNR)$ .

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7:3

3:7

4:5

5:4

answer is B.

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Detailed Solution

It is given that,

P M : M R = 3 : 4

and

L M | | Q R

Δ P L M & Δ P Q R

L M | | Q R

∠ P L M = ∠ P Q R ∠ P M L = ∠ P R Q

Thus,

Δ P L M ~ Δ P Q R

with AA similarity.
We can use the property of similar triangles that their corresponding sides are within the same ratio.
We can write according to the given conditions that

P M M R = 34 P M P R = 37 L M Q R = 37

Similarly, by using the area property of similar triangles we can write that,

a r Δ L M N a r Δ M N R = L M Q R = 37

The value is 3:7.
Hence, the correct option is 2.

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