The sum of the legs of a right-angled triangle is 49, its hypotenuse is 41. Find its area.

Let’s say that one leg is x, then the second leg is 49 – x.

Let’s use the Pythagorean theorem and compose the following equation:

x² + (49 – x) ² = 41²,

х² + 2401 – 98 * х + х² = 1681,

2 * x² – 98 * x + 2401 – 1681 = 0,

2 * x² – 98 * x + 720 = 0,

x² – 49 * x + 360 = 0.

The discriminant of this quadratic equation is:

(-49) ² – 4 * 1 * 360 = 961.

Hence, the equation has the following roots:

x = (49 – 31) / 2 = 9 and x = (49 + 31) / 2 = 40.

Therefore, the second leg of this triangle is:

49 – 9 = 40 or 49 – 40 = 9.

Thus, the area of the triangle is:

S = (40 * 9) / 2 = 180.