The perimeter of a right-angled triangle is 24 cm, and the sum of the lengths of its legs is 14 cm. Calculate the area of this triangle.

Let the smaller leg have a length of x cm, then the second leg will have a length of (14 – x) cm. By the Pythagorean theorem, we obtain the equation: x ^ 2 + (14 – x) ^ 2 = (24 – 14) ^ 2;
x = 6 cm; 14 – 6 = 8 cm. The area of the triangle is equal to half the product of the legs: 6 ∙ 8/2 = 24 (cm ^ 2).
Answer: The area of the triangle is 24 cm ^ 2.