$△ A B C$ is right angled at $A$ . If $B C = 60 c m$ and $A C = 61 c m$ , then AB=____ cm.

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Solution

In a right angle triangle, Pythagoras Theorem states that the sum of the squares of the sides containing the right angle is equal to the square of the hypotenuse.
Therefore, $A B^{2} + A C^{2} = B C^{2}$
Thus, $A B^{2} = B C^{2} - A C^{2}$
$A B^{2} = 61^{2} - 60^{2}$
$A B^{2} = 3721 - 3600$
$A B^{2} = 121$
$A B^{2} = 11^{2}$
$A B = 11 c m$

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