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

Given:
treug. ABC
angle A – straight
AB = a, AC = b – legs
AB = 12 cm
BC = c = 13 cm

Since the triangle is rectangular, we use the Pythagorean theorem c ^ 2 = a ^ 2 + b ^ 2
13 ^ 2 = 12 ^ 2 + b ^ 2
13 ^ 2 – 12 ^ 2 = b ^ 2
(13-12) (13 + 12) = b ^ 2
25 = b ^ 2
b = √25
b = 5
AC = b = 5 (cm) – length of the second leg

The area of a right triangle is equal to half the product of the legs of the triangle
S = 1/2 AB * AC
S = 1/2 12 * 5
S = 60/2
S = 30
30 (cm ^ 2) – area of triangle ABC

Answer: 5 cm and 30 cm ^ 2