As shown in the figure, the length of each side of △ ABC is 24cm. Use the line segment shown in the figure to divide the triangle into four triangles with equal area, and find the sum of the lengths of the line segments CE and & nbsp; CF

As shown in the figure, the length of each side of △ ABC is 24cm. Use the line segment shown in the figure to divide the triangle into four triangles with equal area, and find the sum of the lengths of the line segments CE and & nbsp; CF

According to the question stem, we can get: the area of △ abd = △ BDE = △ def = △ EFC, (1) the area ratio of △ abd and △ BDC is 1:3, according to the property that the area is proportional to the bottom when the height of the triangle is one, we can get: AD: DC = 1:3; because AC = 24 cm, we can get CD = 24 × 34 = 18 (CM); (2) the area ratio of △ def and △ DFC is 1:1, according to the height of the triangle When the height is one, the area is proportional to the bottom: DF: FC = 1:1; because DC = 18 cm, CF = 18 × 12 = 9 (CM); (3) the area ratio of △ BDE and △ EDC is 1:2; according to the height of the triangle, the area is proportional to the bottom: be: EC = 1:2; because BC = 24 cm, CE = 24 × 23 = 16 (CM); 9 + 16 = 25 (CM), a The sum of the length of CF and CE is 25cm