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 ratio of the area 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