Pythogoras theorem

Pythagoras Theorem is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle.

Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas.

Pythagoras Theorem Statement

Pythogoras Theorem

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

Consider the triangle $ABC$ in the figure where side $AB$ is called as perpendicular , side $BC$ is called as base , side $AC$ is called as hypotenuse.

According to Pythogoras theorem

Square of the perpendicular + Square of the base = Square of the hypotenuse

$AB^{2}+BC^{2}=AC^{2}$

Examples

1. Consider a right-angled triangle. The measure of its hypotenuse is 20 inches. One of the sides of the triangle is 16 inches. What would be the measure of the third side?

Let $x$ be the measure of the third side.

According to Pythogoras theorem

Square of the perpendicular + Square of the base = Square of the hypotenuse

$16^{2}+x^{2}=20^{2}$

$x^{2}=20^{2}-16^{2}$

$x^{2}=400-256=144$

$x={\sqrt {144}}=12$

Measure of the third side = $12$ inches.

2. Consider a right-angled triangle. One of the sides of the triangle is 8 cms , other side of the triangle is 6 cms. What would be the measure of the hypotenuse side?

Let $x$ be the measure of the hypotenuse side.

According to Pythogoras theorem

Square of the perpendicular + Square of the base = Square of the hypotenuse

$8^{2}+6^{2}=x^{2}$

$x^{2}=64+36$

$x^{2}=100$

$x={\sqrt {100}}=10$

Measure of the hypotenuse side = $10$ cms