The length of one of the legs of a right-angled triangle is 112 cm and the hypotenuse is 113 cm. Calculate the area of the triangle.

Let’s denote by x the unknown leg of this right-angled triangle.
According to the condition of the problem, the hypotenuse of this right-angled triangle is 113 cm, and one of the legs of this triangle is 112, therefore, using the Pythagorean theorem, we can compose the following equation:
x² + 112² = 113².
We solve the resulting equation:
х² = 113² – 112²;
x² = (113 – 112) * (113 + 112);
x² = 1 * 225;
x² = 225;
x² = 25².
The resulting equation has two roots x = 5 and x = -5. Since the length of the leg of a right-angled triangle is positive, the value x = -5 is not suitable.
Therefore, the second leg of this right-angled triangle is 5 cm.
Find the area S of a given right-angled triangle:
S = (1/2) * 112 * 5 = 56 * 5 = 280 cm².

Answer: the area of ​​this rectangular is 280 cm².