这是一个边长为177×176的矩形被分割为编号A-K的11个正方形,您能算出每个正方形的边长各是多少吗?

Question

这是一个边长为177×176的矩形被分割为编号A-K的11个正方形,您能算出每个正方形的边长各是多少吗?

Answer 1

设边长为：H = a; I = b; C = c;
则
J = a + b; K = a + 2b; F = a + 3b; G = 2a + b; E = 3a + b; D = 5a + 2b; B = c + a + 3b; A = 2c + a + 3b;
由图可知
A + D = 176 所以 2c + 6a + 5b = 176
A + B = 177 所以 3c + 2a + 6b = 177
D + E + F = 177 所以 9a + 6b = 177
三个方程,三个未知数
解得 a = 9; b = 16; c = 21
所以 A = 99; B = 78; C = 21; D = 77; E = 43; F = 57; G = 34; H = 9; I = 16; J = 25; K =41;