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Introduction The Pythagorean theorem is a fundamental principle of geometry that has helped mathematicians and problem solvers for centuries.

 This theorem, named after the ancient Greek mathematician Pythagoras,  establishes the relationship between the sides of a right triangle.

 This article explains what the Pythagorean theorem is and how to use it effectively in different scenarios.

 Understanding  Pythagorean Theorem  Pythagorean Theorem can be expressed as:

a² + b² = c²

In this formula: ``a'' and ``b'' are the lengths of the two short sides.

 Right triangle (leg). c" is the length of the longest side,  the hypotenuse.

This theorem applies only to right triangles where one of the angles is exactly 90 degrees.

 It helps to find the length of one side if you know the other two sides.

 Using the Pythagorean Theorem Find the hypotenuse: If you know the lengths of the legs, you can use the theorem to calculate the hypotenuse.

 Simply square  "a" and "b", add them, and take the square root of the sum to find "c".

 Example: If you have a right triangle and one leg is 3 units long and the other leg is 4 units long,

you can use the theorem to find the hypotenuse.

 a² + b² = c²

3² + 4² = c²

9 + 16 = c²

25 = c²

c = √25

c = 5

Therefore, the length of the hypotenuse is 5 units.

 Find the length of a leg: Given the length of one leg and the hypotenuse, you can find the length of the other leg.

 Similarly use sentences, this time resolving 'a' or 'b'.

 Example: If the length of the hypotenuse of a right triangle is 10 units and the length of one leg is 6 units, you can find the length of the other leg.

 a² + b² = c²

a² + 6² = 10²

a² + 36 = 100

a² = 100 - 36

a² = 64

a = √64

a = 8

Therefore, the length of the other leg is 8 units.

 Checking for  Right Triangles: You can also use the theorem to determine whether a triangle is a right triangle.

 If a² + b² = c², we get a right triangle.

 If not, the triangle is not a right triangle.

 Applications of  Pythagorean Theorem The Pythagorean Theorem has applications other than geometry.

 It is widely used in engineering, physics, and various other fields to solve real-world problems involving distance, speed, etc.

 For example, it is used in navigation to calculate distances or in computer graphics to determine the distance between two points in two-dimensional space.

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Practice Questions for you

1. If the length of the hypotenuse of a right triangle is 25 units and the length of one leg is 36 units, you can find the length of the other leg.

2. If you have a right triangle and one leg is 12 units long and the other leg is 16 units long,