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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Straight Lines

Olympiad workbook · IOQM · Straight Lines

Three parallel lines L_1, L_2, L_3 are drawn in the plane such that...

Three parallel lines L1,L2,L3L_1, L_2, L_3 are drawn in the plane such that the perpendicular distance between L1L_1 and L2L_2 is 3 and the perpendicular distance between L2L_2 and L3L_3 is also 3 . A square ABCDA B C D is constructed such that AA lies on L1,BL_1, B lies on L3L_3 and CC lies on L2L_2.Find the area of the squareThree parallel lines L_1, L_2, L_3 are drawn in the plane such that the perpendicular distance between L_1 and L_2 is 3

Correct answer

45

Step-by-step solution

Three parallel lines L_1, L_2, L_3 are drawn in the plane such that the perpendicular distance between L_1 and L_2 is 3
sin⁡θ=3a and cos⁡θ=6a9a2+36a2=1⇒a2=45\begin{aligned} & \sin \theta=\frac{3}{a} \text { and } \cos \theta=\frac{6}{a} \\ & \frac{9}{a^2}+\frac{36}{a^2}=1 \Rightarrow a^2=45\end{aligned}
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