Question

A cardboard rectangle is cut out and the midpoint of one side is joined to the other ends to make a triangle. If you randomly put a dot in the rectangle, what is the probability that it would be within the triangle?

Answer 1

The triangle and the rectangle have the same base and height.so, the area of the triangle is half the area of the rectangle.

Hence the probability of the dot falling inside the triangle = $\frac{Areaofthetriangle}{Areaofrectangle}$

Let the base be $x$ and the height( breadth ) be $y$

Area of rectangle = $x\times y$

Area of triangle = $\frac{1}{2}x\times y$

Hence Probability of the dot falling inside the triangle = $\frac{\frac{1}{2}x\times y}{x\times y}$ = $\frac{1}{2}$