【趣味数学题】 新算额题（三） Revival of Sangaku 3

郑涛提出的问题

图：如图 1 ，黄色、蓝色和红色三角形在一个点 P 相交 。穿过 P 的三条线平行于三角形 ABC 的边（AB, AC, BC）。

命题：假设黄色三角形、蓝色三角形和红色三角形的面积分别为4、9、49。问：三角形ABC的面积是多少？

Problem created by Tao Steven Zheng

Diagram: Consider triangle ABC in Figure 1. There are three triangles coloured yellow, blue, and red that meet at one point P. The lines through P are parallel to the sides of triangle ABC.

Problem: Given that the area of the yellow triangle, blue triangle, and red triangle are 4, 9, and 49 respectively, determine the area of triangle ABC.