In a right-angled triangle, the legs of which are 8 and 6, the height is lowered from the vertex of the right angle

In a right-angled triangle, the legs of which are 8 and 6, the height is lowered from the vertex of the right angle to the hypotenuse. Find the difference between the areas of the larger and smaller triangles by which the height divides the given triangle.

Since, by definition, the height is perpendicular to the hypotenuse, it will divide the original triangle into two right-angled triangles, with hypotenuses 8 and 6 and leg h. The second legs are equal respectively:
√ (8 ^ 2 – h ^ 2) and √ (6 ^ 2 – h ^ 2).
Then their areas are equal:
1/2 * h * √ (8 ^ 2 – h ^ 2) and 1/2 * h * √ (6 ^ 2 – h ^ 2).
The area difference S will be:
S = 1/2 * h * (√ (8 ^ 2 – h ^ 2) – √ (6 ^ 2 – h ^ 2)).