In a right-angled triangle, the legs are 8 and 6 cm. Find the hypotenuse and area of a right triangle.

Let’s denote by c – the hypotenuse of a right triangle, and by a and b – legs. Then, by the Pythagorean theorem: c ^ 2 = a ^ 2 + b ^ 2 or c = √ (a ^ 2 + b ^ 2).

In this case, to determine the area of a right-angled triangle, we will use the formula: S = 1/2 * a * b. The area of a right-angled triangle is half the product of the legs.

Substitute the given values and determine the values:

c = √ (8 ^ 2 + 6 ^ 2) = √ (64 + 36) = √100 = √10 ^ 2 = 10 (cm);

S = 1/2 * 8 * 6 = 1/2 * 48 = 48/2 = 24 (cm2).

Answer: The hypotenuse is 10 centimeters, the area is 24 square centimeters.