# Practice Math With Us # Pythagorean Theorem Squares

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 area2 = Opposite area2 +  Adjacent area2

## 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 area2 = Opposite area2 +  Adjacent area2

= 142 + 152

= 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 area2 = Opposite area2 +  Adjacent area2

Adjacent area2 = Hypotenuse area2 - Opposite area2

= 152 - 132

= 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.