In figure the segment $S T$ is parallel to side $P R$ of $△ P Q R$ and it divides the triangle into two parts of equal area. Find the ratio $\frac{P S}{P Q}$ .

1 : 2

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1 : 8

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1 : 4

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1 : 10

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Solution

The correct option is A $1 : 2$
$P R$ is $10 + 0 S T$
So, $\frac{P S}{P Q} = \frac{R T}{R Q}$
using mid point theorem
$T$ is the midpoint of $R Q$
$∴ R T = T Q$
$\frac{P S}{P Q} = \frac{R T}{2 R T}$
$\Rightarrow \frac{P S}{P Q} = \frac{1}{2}$
$P S : P Q = 1 : 2$

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