Triangle ABC is similar to triangle PQR and AB : PQ= 2 : 3. AD is median to the side BC in triangle ABC and PS is the median to side QR in triangle PQR. What is the value of ( BD QS )^2?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\frac{AB}{PQ}=\frac{2}{3}\left(\text{Given}\right)$$

$$\begin{array}{rl}& \frac{\text{area of }\Delta ABC}{\text{area of }\Delta PQR}={\left(\frac{AB}{PQ}\right)}^2=\frac{4}{9}\\ & \left[\text{Ratio of similar }\Delta \right]\\ & \frac{\text{area of }\Delta ABD}{\text{area of }\Delta PQS}=\frac{\frac{1}{2}\times \text{area of }\Delta ABC}{\frac{1}{2}\times \text{area of }\Delta PQR}\\ & =\frac{4}{9}=\frac{B{D}^2}{Q{S}^2}\\ & \left[\therefore AD\&PS\text{are median}\right]\end{array}$$