The hypotenuse of a right-angled triangle is 10 cm, and its area is 24 cm. Find its legs.

Let the legs of the triangle be equal to a and b, and the hypotenuse is equal to c. Area C = a * b / 2 = 24 cm2. Whence a * b = 2 * 24 = 48 cm2. (one)

c ^ 2 = a ^ 2 + b ^ 2 = (10) ^ 2; a ^ 2 + b ^ 2 = 100. (2)

Add (2) and 2 * (1), we get: a ^ 2 + b ^ 2 + 2 * a * b = 100 + 2 * 48 = 100 + 96 = 196. (a + b) ^ 2 = 196; (a + b) = √196 = 14.

Subtract (2) – 2 * (1). a ^ 2 + b ^ 2 – 2 * a * b = 100 – 2 * 48 = 100 – 96 = 4; a – b = √4 = 2.

Received: a – b = 2; a + b = 14, add up, we get 2 * a = 2 + 14 = 16, a = 16: 2 = 8, b = 14 – 8 = 6. Check: c = √ (8 ^ 2 + 6 ^ 2) = √100 = 10.

Answer: a = 8; h = 6.