一个毕达哥拉斯三元组，其两个数字是 8 和 10，那么第三个数字是多少？

为直角三角形定义了毕达哥拉斯定理。毕达哥拉斯定理定义了直角三角形各边之间的关系。该定理也称为勾股定理，定义为“斜边的平方等于其他两条边、垂线和底边的平方和。”直角三角形的垂线和底是相互成90°的两条边，斜边称为第三边。

毕达哥拉斯公式

该公式是在定理的帮助下定义的，如果斜边的平方等于直角三角形其他两条边的平方和，则

(Hypotenuse)² = Perpendicular² + Base²

H² = P² + B² 

$H= \sqrt{P^2+B^2}$

示例：在直角三角形中，相互成 90° 的两侧的值分别为 m 和 3m。求三角形第三边的值。

解决方案：

The sides that are 90° to each other will be perpendicular and base and the third side that is required to be found is the hypotenuse.

Therefore, P=m, B= 3m, H=?

The formula for Pythagoras theorem is,

H² = P² +B²

H² = m² +(3m)²

H² = m² + 9m²

H² = 10m²

H = √10 m

毕达哥拉斯三元组的两个数字是 8 和 10，那么第三个数字是多少？

The above question is very interesting as the values of two sides are given, but it is not given that if the sides are hypotenuse, perpendicular or base. Let’s say that the triplets are required to be written as (x, 8, 10), x is the unknown triplet.

Since, 10 is the largest number given in the question and hypotenuse is the largest side, lets assume that hypotenuse is 10 units and perpendicular is 8 units.

According to the formula for Pythagoras theorem,

H² = P² +B²

10² = 8² + x²

100 = 64 + x²

x² = 100 – 64

x² = 36

x = √36

x = 6 units.

Hence, the triplets are (6, 8, 10).