Question

In a $	riangle PQR$, point $X$ is on $PQ$ and point $Y$ is on $PR$ such that $XP = 1.5$ units, $XQ = 6$ units, $PY = 2$ units and $YR = 8$ units. Consider the following statements : Statement I : $QR = 5 XY$ Statement II : $	riangle PYX$ is similar to $	riangle PRQ$ In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

A. Here, $PX/XQ = 1.5/6 = 1/4 \implies PX/PQ = 1.5/7.5 = 1/5$. $PY/YR = 2/8 = 1/4 \implies PY/PR = 2/10 = 1/5$. Since $PX/PQ = PY/PR = 1/5$ and $\angle P$ is common, $	riangle PYX \sim 	riangle PRQ$. Thus, Statement II is true. Also, $XY/QR = 1/5 \implies QR = 5 XY$, so Statement I is true.

Properties of Similar Triangles

Explanation

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