Question

What is the area of the largest triangle that can be fitted into a rectangle of length l units and width w units?

• A. $\frac{lw}{2}$
• B. $\frac{lw}{3}$
• C. $\frac{lw}{4}$
• D. $\frac{lw}{6}$

Answer 1

The correct option is A

$\frac{lw}{2}$

Determining the area of the largest triangle.

Let ABCD be rectangular in length $l$ and width $w$ Now, we construct a triangle of maximum area inside it in all possible ways-
Maximum base length $=l$
Maximum height $=w$

Using the formula for the area of a triangle

$$\begin{gathered} Area=\frac{1}{2}\times Base\times Height \\ \Rightarrow =\frac{1}{2}\times l\times w \\ \Rightarrow =\frac{lw}{2} \end{gathered}$$

Hence, the correct choice is “Option A”.