Show a triangle on a pegboard Think of the triangle as made

Show a triangle on a pegboard. (Think of the triangle as made out of a rubber band, which is stretched around three pages.) Describe or draw at least two ways to move point C of the triangle to another peg (keeping points A and B fixed) in such a way that the area of the new triangle is the same as the area of the original triangle. Explain your reasoning.

Solution

Area of triangle = (0.5)(base)(height).

Here base AB remains constant

So, for area to remain constant height to remain constant which gives that the point C must lie at same vertical distance from AB as in the given figure.

all the points in the horizontal line passing through C have same perpendicular distance on AB.

Area remains constant by moving the point C horizontally right or left/