Properties Of Triangles Ques 60
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) $1: 8$
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Answer:
Correct Answer: 60.(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 $1: 4$.
BETA
