Edited by Richard Walker, Sunday, 13 July 2025, 22:52
"The base of a triangle is 12 cm. What is the length of the line that is drawn parallel to the base so that the area of the triangle is divided into two equal parts?"
This popped up in my inbox, together with a longish solution that brought in the heights of the two regions, the triangle and the trapezium, and used similar triangles.
But there is a shorter and I would argue more insightful approach. If we look at a sketch of the problem
we see the small triangle is a scaled version of the big one. The scale factor of the distances is x : 12 and so the scale factor of area is x2 : 144. But this must be 1 : 2 since the small triangle has half the area. So
Found on Quora
"The base of a triangle is 12 cm. What is the length of the line that is drawn parallel to the base so that the area of the triangle is divided into two equal parts?"
This popped up in my inbox, together with a longish solution that brought in the heights of the two regions, the triangle and the trapezium, and used similar triangles.
But there is a shorter and I would argue more insightful approach. If we look at a sketch of the problem
we see the small triangle is a scaled version of the big one. The scale factor of the distances is x : 12 and so the scale factor of area is x2 : 144. But this must be 1 : 2 since the small triangle has half the area. So