question_answer

Two similar parallelograms have corresponding sides the ratio 1 : k What is the ratio of their

A)  \[1:3{{k}^{2}}\]

B)  \[1:4{{k}^{2}}\]

C)  \[1:{{k}^{2}}\]

D)  \[1:2{{k}^{2}}\]

Correct Answer: C

Solution :

Let the sides of a parallelogram are x, y and xk, yk,. Since, sides of two parallelogram are in 1 : k \[\Delta ABC\sim \Delta PQT\] \[\frac{AC}{PT}=\frac{BC}{QT}\]\[\Rightarrow \]\[\frac{BC}{QT}=\frac{y}{yk}=\frac{1}{k}\] Let \[BC=z\] and \[QT=zk\] Ratio of areas of two similar parallelogram are in \[=\frac{xz}{zk+zk}=\frac{1}{{{k}^{2}}}\]