Question

Question 4

What is the area (in sq units) 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) $\frac{lw}{6}$ (d) $\frac{lw}{4}$

Answer 1

Let ABCD be the rectangle of length l and width w.
Now, we construct a triangle of maximum area inside it in all possible ways.
$\because$ We know that,
Area of triangle $=\frac{1}{2}\times Base\times Height$
So, for maximum area, base and height of maximum length is needed.
Here, maximum base length = l
and maximum height = w
$\therefore$ Area (maximum) of triangle $=\frac{1}{2}\times l\times w=\frac{l\times w}{2}squnits$