MATLAB--CUP Challenge（杯赛挑战）

例1.

Problem 1974. Length of a short side

Calculate the length of the short side, a, of a right-angled triangle with hypotenuse of length c, and other short side of length b.

（计算直角三角形的短边 a 的长度，其中斜边长度为 c，另一短边长度为 b。）

% 输入斜边长度和另一短边长度
c = input('Enter the length of the hypotenuse (c): ');
b = input('Enter the length of the other short side (b): ');

% 计算短边a的长度
a = sqrt(c^2 - b^2);

% 显示结果
fprintf('The length of the short side (a) is: %.2f\n', a);

例2

 Problem 2024. Triangle sequence

A sequence of triangles is constructed in the following way:

1) the first triangle is Pythagoras' 3-4-5 triangle

2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle

3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.

Each triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.

What is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?

（这个序列的三角形是按照以下方式构造的：

1）第一个三角形是毕达哥拉斯的3-4-5三角形。

2）第二个三角形是一个直角三角形，其第二长边是第一个三角形的斜边，而最短边与第一个三角形的第二长边相同。

3）第三个三角形是一个直角三角形，其第二长边是第二个三角形的斜边，而最短边与第二个三角形的第二长边相同，依此类推。

序列中的每个三角形都是这样构造的：其第二长边是前一个三角形的斜边，而其最短边与前一个三角形的第二长边相同。 求第n个三角形的斜边作为边长的正方形的面积是多少？）

以下是用 MATLAB 编写的程序，用于计算序列中第 n 个三角形的斜边作为边长的正方形的面积：

function area = squareArea(n)
    % Initialize the first triangle (3-4-5 triangle)
    a = 3;
    b = 4;
    c = 5