In a right-angled triangle, the legs are 3: 4, the height divides it into two triangles, the difference in area of which

In a right-angled triangle, the legs are 3: 4, the height divides it into two triangles, the difference in area of which is 56 decimeters squared. Find the area of a given triangle

Let one leg be 3x, then the other – 4x. By the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2 = 9x ^ 2 + 16x ^ 2 = 25x ^ 2 or is it (5x) ^ 2
Then the hypotenuse of this triangle is 5x.
We know that the height in a right-angled triangle divides it into two triangles similar to the original. Then their coefficients of similarity, based on the found hypotenuse, are 3/5 and 4/5. We know that the areas of similar triangles are related as the square of their similarity coefficients. Let us denote the area of the original triangle by S. Then:
(4/5) ^ 2 * s – (3/5) ^ 2 * s = 56
We get the equation:
4 * s / 25 = 56
Then s is 450.
Answer: 450