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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) lw2 (b) lw3
(c) lw6 (d) lw4

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Solution

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.
We know that,
Area of triangle =12×Base×Height
So, for maximum area, base and height of maximum length is needed.
Here, maximum base length = l
and maximum height = w
Area (maximum) of triangle =12×l×w=l×w2sq units


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