Straight LineHardBloom L3
Question
Given a triangle whose vertices are at $(0,0),(4,4)$ and $(10,0)$. A square is drawn in it such that its base is on the $x$-axis and its two corners are on the 2 sides of the triangle. The area of the square is equal to :
Options
A.$\frac{400}{49}$
B.$\frac{400}{25}$
C.$\frac{625}{16}$
D.$\frac{625}{49}$
Solution
Sol. [Key Concept: Inscribed square with base on the $x$-axis: similar triangles give the side, hence the area.]
$(2a,a)$ lies on $2x + 3y = 20$
So $4a + 3a = 20$
$$\begin{matrix} \Rightarrow & a = \frac{20}{7} \\ \therefore & \text{~}\text{Area}\text{~} = \frac{400}{49} \end{matrix}$$
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