In a right-angled triangle ABC, the height CD drawn to the hypotenuse AB divides this hypotenuse in the ratio

In a right-angled triangle ABC, the height CD drawn to the hypotenuse AB divides this hypotenuse in the ratio AD: DB = 1: 4. Find the area of triangle ABC if CD = 32 cm

Consider a triangle СDA, AD = x, AC2 = X2 + 1024
Consider a triangle СDВ, ВD = 4x, BC2 = 16×2 + 1024
25×2 = AB2 = AC2 + BC2 = 17×2 + 2048
8×2 = 2048
x2 = 256
x = 16
AC2 = 256 + 1024 = 1280
AC = root of 1280 = 16 roots of 5
BC2 = 16 * 256 + 1024
BC = 32 roots of 5
Area = 1/2 * 16 * 32 * 5 = 1280