Find the area of a right-angled triangle if its height divides the hypotenuse into 20 cm and 16 cm segments.

1. Vertices of the triangle – A, B, C. AE – height. BE = 20 centimeters. CE = 16 centimeters.

∠А = 90 °. S is the area of the triangle.

2. In a right-angled triangle (according to its properties), the length of the height drawn from the vertex of the right angle to the hypotenuse is calculated by the formula:

3. AE = √BE x CE.

AE = √ BE x CE = √20 x 16 = √4 x 5 x 16 = 8√5 centimeters.

4. BC = BE + CE = 20 + 16 = 36 centimeters.

5. S = BC / 2 x AE = 36/2 x 8√5 = 144√5 centimeters²

Answer: S equals 144√5 centimeters²