Geometry Question: Triangle Area

This aptitude practice question is a geometry and mensuration question. Concept tested: Area of triangle inscribed in a rectangle.

Question

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

1. \\frac{lw}{3})
2. \\frac{2lw}{3})
3. \\frac{3lw}{4})
4. \\frac{lw}{2})

  Correct Answer      Choice (4). \\frac{1w}{2})

Explanatory Answer

The triangle which has its base as the length of the rectangle and its height as the width of the rectangle is the largest triangle that can be fitted in the triangle.

Alternatively, the triangle which has its base as the width of the rectangle and its height as the length of the rectangle will be the largest triangle that can be fitted in the rectangle.

The area computed in both the instances will be same.

If the base of the triangle is 'l' and its height 'w', then its area is \\frac{lw}{2}) square units.
Alternatively, if the base of the triangle is 'w' units and its height is 'l' units, then its area is \\frac{wl}{2}) square units.

  The correct answer is Choice (4).