Properties of Triangles 3 Question 8
8. The ratio of the areas of $\triangle P Q S$ and $\triangle P Q R$ is
(a) $1: \sqrt{2}$
(b) $1: 2$
(c) $1: 4$
(d) $1: 8$
Objective Questions II
(One or more than one correct option)
Show Answer
Answer:
Correct Answer: 8. (c)
Solution:
- Coordinates of $P$ and $Q$ are $(1,2 \sqrt{2})$ and $(1,-2 \sqrt{2})$.
Now, $P Q=\sqrt{(4 \sqrt{2})^{2}+0^{2}}=4 \sqrt{2}$
Area of $\triangle P Q R=\frac{1}{2} \cdot 4 \sqrt{2} \cdot 8=16 \sqrt{2}$ sq units
Area of $\triangle P Q S=\frac{1}{2} \cdot 4 \sqrt{2} \cdot 2=4 \sqrt{2}$ sq units
Ratio of areas of $\triangle P Q S$ and $\triangle P Q R$ is $1: 4$.
