Straight Lines
Equilateral Triangle Between Parallel Lines — Area
nta_pyq_2026_jan
Grade 11
Question:
Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle $ABC$, where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$, respectively, is:
Step-by-Step Solution
Key Concept: Let $L_2:y=0$, $L_1:y=9$ (separation 9). $A=(0,3)$. $B=(x_B,9)$, $C=(x_C,0)$. Equilateral: $AB=AC=BC$. Compute $AB^2=x_B^2+36$, $AC^2=x_C^2+9$, $BC^2=(x_B-x_C)^2+81$.
Area $=21\sqrt{3}$.
Correct Answer: 2