If the perimeter of a diamond is 20cm and the ratio of two diagonals is 4:3, the area of the diamond is () A. 12cm2B. 24cm2C. 48cm2D. 96cm2

If the perimeter of a diamond is 20cm and the ratio of two diagonals is 4:3, the area of the diamond is () A. 12cm2B. 24cm2C. 48cm2D. 96cm2

Let the diagonals of the diamond be respectively 8x and 6x. It is known that the perimeter of the diamond is 20cm, so the side length of the diamond is 5cm. According to the properties of the diamond, the diagonals of the diamond are divided vertically, that is, (4x) 2 + (3x) 2 = 25. The solution is x = 1, so the diagonals of the diamond are respectively 8cm and 6cm, so the area of the diamond is 12 × 8 × 6 = 24cm2, so B