The leg of a right-angled triangle is 20 cm, and its projection onto the hypotenuse is 16 cm, find the area of the triangle.

1. Vertices of the triangle – A, B, C. S – the area of the triangle. ∠А = 90 °. Leg AB = 20 cm.

BE = 16 cm. AE – height.

2. Calculate the length of the height AE using the Pythagorean theorem:

AE = √AB² – BE² = √20² – 16² = √400 – 256 = √144 = 12 cm.

3. The length of the height AE, according to the properties of a right-angled triangle, is calculated by

formula:

AE = √BE x CE.

AE² = BE x CE.

4. CE = AE²: BE = 12²: 16 = 144: 16 = 9 cm.

5. BC = BE + CE = 16 + 9 = 25 cm.

6. S = BC / 2 x AE = 25/2 x 12 = 150 cm².