Pythagorean Theorem - Essay Example

“The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides” (Audy & Morosini, 2007). Hence, the Pythagorean Theorem can be used to find out the length of the side of a right angled triangle when the lengths of the two other sides are known. The theorem has a range of real life applications. For instance, it can be used to measure the distance between two cities in a map, height of an object from the length of its shadow, the length of the diagonal of a rectangle and for many other purposes.

The longest side of a triangle is called hypotenuse, while the remaining two sides are called the legs of the triangle. The algebraic expression of the Pythagorean Theorem can be written as follows: As Sonnenberg, Wittenberg, Ferrucci, Mueller and Simeone (1981) point out, the Pythagorean Theorem is helpful to calculate the unknown length of a side of a right angled triangle, if the lengths of the other two sides are known. Similarly, in a right angled triangle, the length of the hypotenuse is greater than other two sides, but less than the sum of their lengths.

The above figure contains four copies of a right angled triangle having sides a, b, and c; which are arranged in a square having side c. Hence, each triangle has an area of ½ab whereas the small square has a side b-a and an area (b – a) 2. Hence, the area of the large square becomes, It has been proved that the converse of this theorem is also true. Hence, for any triangle with sides a, b, and c; and a2 + b2 = c2, the angle between the legs a and b will be a right angle (90o) (cited in Serra, 1994).

In total, Pythagorean Theorem is one of the fundamental theorems of mathematics. The theorem has a range of proofs and its converse is also true. Above all, it has a wide range of applications in the real life. Sonnenberg, E. V., Wittenberg, J., Ferrucci, J. T., Mueller, P. R. & Simeone, J. F. (1981).