Pythagoras Theorem

Theorem

In a right angled triangle, the square of hypotenuse is equal to the sum of the square of other two sides.

Right angle \(\triangle ABC\)
Right angle \(\triangle ABC\)

In the above right angle \(\triangle ABC\), p is perpendicular, b is base and h is hypotenuse.

\(h^2 = b^2 + p^2\)

or \(h = \sqrt{b^2 + p^2}\)

Example

Find the length of hypotenuse of right angle \(\triangle ABC\), where length of base =3cm and length of perpendicular = 9cm.

Solution:

In \(\triangle ABC\)

b=3cm

p=4cm

\(\because \), \(\triangle ABC\) is a right angle triangle          (given)

\(\therefore \) by applying Pythagoras theorem

\(h = \sqrt{b^2 + p^2}\)

\(h = \sqrt{3^2 + 4^2}\)

\(h = \sqrt{9 + 16}\)

\(h = \sqrt{25}\)

\(\therefore \) \(h = 5cm\)

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