Question

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? (2 marks)

Answer 1

Let ABCD be the rectangle of length $l$ units and width $w$ units.
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Now, we construct a triangle of maximum area inside it in all possible ways.

We know that,
Area of triangle $=\frac{1}{2}\times Base\times Height$

So, for maximum area, base and height of maximum lengths are needed.
Maximum base length $=l$
Maximum height length $=w$ (1 mark)

$\therefore$ Area (maximum) of triangle $=\frac{1}{2}\times l\times w=\frac{l\times w}{2}$ sq units (1 mark)