The hypotenuse of a right-angled triangle is 41. The leg opposite to it is 9. Find the area

By the condition of the problem, it is known that the hypotenuse of a right-angled triangle is C = 41, and the length of one of the legs is B = 9.

Let us denote the length of the second leg by A.

Then, by the Pythagorean theorem, we calculate the length of the second leg:

A ^ 2 + B ^ 2 = C ^ 2,

A ^ 2 = C ^ 2 – B ^ 2 = (C – B) * (C + B) = (41 – 9) * (41 + 9) = 32 * 50 = 16 * 100,

A ^ 2 = 16 * 100,

A = 4 * 10 = 40.

Consequently, the area S of this triangle is equal to half the product of the legs:

S = 1/2 * A * B = 1/2 * 40 * 9 = 20 * 9 = 180.

Answer: the area of the triangle is S = 180.