Question

In the figure (not drawn to scale) given below, P is a point on AB such that $AP : PB = 4 : 3$. PQ is parallel to AC and QD is parallel to CP. In $\triangle ARC$, $\angle ARC = 90^\circ$, and in $\triangle PQS$, $\angle PQS = 90^\circ$. The length of QS is 6 cm. What is the ratio of $AP : PD$?

• A. 10 : 3
• B. 2 : 1
• C. 3 : 7
• D. 8 : 3

Hint:

For problems involving similar triangles, use the properties of parallel lines and proportionality to calculate the ratios of the sides.

Answer 1

The Correct Option is D

Given that PQ is parallel to AC and QD is parallel to CP, we can use similar triangles and the properties of parallel lines to determine the ratio of $AP : PD$. Since $\triangle ARC$ is a right triangle, and $\triangle PQS$ is also a right triangle, by the properties of similar triangles, the sides of these triangles will be proportional. From the given information, we know that the length of $QS$ is 6 cm. By applying the proportionality of the sides of the triangles and using the ratio of $AP : PB = 4 : 3$, we find that the ratio of $AP : PD$ is 8 : 3.