Find the area of a parallelogram whose diagonals are 26 and 24 cm, and one of them is perpendicular to the side.

1. Vertices of the parallelogram – А, В, С, D. Diagonal АС = 26 cm. Diagonal ВD = 24 cm. ВD is perpendicular to СD. S is the area of the parallelogram.

2. Taking CD for x, BC for y, we will compose two equations:

3. ВD² + х² = у² (according to the Pythagorean theorem). x² – y² = 24² = – 576.

АС² + ВD² = 2 (х² + у²) (according to the properties of the parallelogram). x² + y² = (AC² + BD²) / 2 = (676 + 576) / 2 = 626.

4. Add these equations:

2x² = 50;

x² = 25;

x = 5.

CD = 5 cm.

5. S = CD x BD = 5 x 24 = 120 cm².

Answer: S equals 120 cm²