Pythagorean theorem is one of the basic fundamental theorem in mathematics. This theorem is suitable for a right angle triangle. Pythagorean theorem says with the length of a side squares of a right angle triangle. The name of a Pythagorean theorem is given by a mathematician Pythagoras, hence it is also called as Pythagoras theorem.

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## Statement of Pythagorean theorem squares:

Statement of Pythagorean theorem squares is as follows.

The square of a hypotenuse area of a right angle triangle is obtained by addition of the squares of other two sides area of triangle. The other two sides are termed as opposite and adjacent side of a right angle triangle.

**Representation of right angle triangle:**

Form the above figure the Pythagorean theorem is,

Hypotenuse area^{2} = Opposite area^{2} + Adjacent area^{2}

## Example problems for Pythagorean theorem squares:

**Example: 1**

The opposite area of right angle triangle is 14 and the adjacent area of right angle is 15.Determine the hypotenuse of a right angle triangle.

**Solution:**

Given,

Opposite area of right angle triangle = 14 m

Adjacent area of right angle triangle = 15 m

Pythagorean theorem is ,

Hypotenuse area^{2} = Opposite area^{2} + Adjacent area^{2}

= 14^{2} + 15^{2}

= 196 + 225.

= 421

Hypotenuse =`sqrt(421)` = 20.51 m

The hypotenuse of a given right angle triangle is 20.51 m.

**Example: 2**

A right angle triangle has opposite side of 13 and hypotenuse side of 15. Find the adjacent side of ar ight angle triangle.

**Solution:**

Given,

Opposite side = 13 m

Hypotenuse side = 15

Hypotenuse area^{2} = Opposite area^{2} + Adjacent area^{2}

Adjacent area^{2} = Hypotenuse area^{2} - Opposite area^{2}

= 15^{2} - 13^{2}

= 225 - 169

= 56

= `sqrt(56)` = 7.48 m.

The adjacent side of a given right angle triangle is 7.48 m.

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## Practice problems for Pythagorean theorem squares:

**Problem: 1**

A right angle triangle has opposite side of 4 and adjacent side area of 3.Determine the hypotenuse side area of a right angle triangle.

**Answer: **5 m

**Problem: 2**

A right angle triangle has opposite side of 12 and adjacent side area of 9. Determine the hypotenuse side area of a right angle triangle.

**Answer: **15