One of the legs of a right-angled triangle is 15 cm, and the median drawn to the hypotenuse is 8.5 cm.

One of the legs of a right-angled triangle is 15 cm, and the median drawn to the hypotenuse is 8.5 cm. Find the area of the triangle.

1) Calculate the length of the hypotenuse, taking into account that it is equal to the length of two medians (property): c = 2 * m, where m is the length of the median (m = 8.5 cm).

c = 2 * m = 2 * 8.5 = 17 cm.

2) Calculate the length of the unknown leg: b = √ (c ^ 2 – a ^ 2), where a is the length of the known leg (a = 15 cm).

b = √ (c ^ 2 – a ^ 2) = √ (17 ^ 2 – 15 ^ 2) = √ (289 – 225) = √64 = 8 cm.

3) Find the required area of the triangle: S = 0.5 * b * a = 0.5 * 8 * 15 = 60 cm2.

Answer: The required area is 60 cm2.