Constant Area of Triangle ABC

Submitted by Jhun Vert on

From the figures shown below. Squares EGHI and KHJB are fixed. Show that the area of triangle ABH is constant regardless of the dimensions of square ADEF.
 

Figure 1

screenshot_2019-08-13_08.07.47.png

 

Figure 2

screenshot_2019-08-13_08.08.16.png

 

Figure 3

screenshot_2019-08-13_08.08.45.png

 

Figure 4

screenshot_2019-08-13_08.09.42.png

 

Tags
Area of Triangle
Square
Oblique Triangle

MONGOL○482 Tue, 08/20/2019 - 18:44

I don't really know how to prove this one sir. I just noticed when i substituted values, by taking line BH as the base, we will be having the same height in all triangles which we all know that if two triangles have the same base and height, their areas will be the same if i will not be mistaken.

MONGOL○482 Tue, 08/27/2019 - 19:39

1. The diagonals of a square are perpendicular to each other.

2. If we draw a line extending diagonal AE of square AFED, we can see that vertex A is still going to land on this line no matter what the size of square AFED.

3. We can also see that diagonal AE is perpendicular to diagonal BH since their bases are parallel on the horizon lets say x.

Having these in mind and setting BH as the base of the triangle, and since vertex A can also land on vertex E, we can say that Area ABH=1/2 (BH)(EG2+GH2)1/2