As shown in the figure, the triangle ABC is a right triangle, the quadrilateral EDFC is a square, the sum of the areas of the two shadow triangles is 32 square centimeters, ad: DB = 4:1, find the length of AD

As shown in the figure, the triangle ABC is a right triangle, the quadrilateral EDFC is a square, the sum of the areas of the two shadow triangles is 32 square centimeters, ad: DB = 4:1, find the length of AD

Because the triangle ABC is a right triangle and the quadrilateral EDFC is a square, so de ∥ BC, DF ∥ AC, de = EC = CF = FD, let the side length of the square EDFC be x, because ad: DB = 4:1, so BF = 14fc = 14x, AE = 4ec = 4x, the sum of the areas of the two shadow triangles is 32 square centimeters, 12bf × FD + 12de × AE = 32, that is, 12 (14x × x) + 12 (x × 4x) = 32, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;               18x2+2x2=32，                       178x2=32，                    &In the right triangle ade, ad2 = AE2 + ED2, = (4x) 2 + X2, = 17x2, ad2 = 162, ad = 16 cm. Answer: the length of ad is 16 cm