One of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 13 cm.

One of the legs of a right-angled triangle is 12 cm, and the hypotenuse is 13 cm. Find the second leg and the area of the triangle.

Let a = 12 cm and b – legs, c = 13 cm – hypotenuse. Let us find leg b by the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
b ^ 2 = c ^ 2 – a ^ 2;
b = √ (c ^ 2 – a ^ 2);
b = √ (13 ^ 2 – 12 ^ 2) = √ (169 – 144) = √25 = 5 (cm).
The area of a right-angled triangle is equal to half the product of its legs:
S = ab / 2;
S = 12 * 5/2 = 60/2 = 30 (cm square).
Answer: S = 30 cm square.