Name: Areas of Similar Triangles
Uploaded: 2019-07-19
Duration: 6 min 54 s
Description: The corresponding sides of similar triangles are proportional. Are the ratios of areas of similar triangles the same as that of their sides? Watch this video...

Question

For a right angle triangle with integer sides at least one of its measurements must be an even number. Why?

Accepted Answer

A right angle triangle always follows Pythagoras Theorem.

So, if $a$ is the hypothenuse, $b$ and $c$ are the other two sides.

By Pythagoras theorem we get,

$a^{2} = b^{2} + c^{2}$

If we assume $a$ is an odd number then $a^{2}$ will also be an odd number because square of an odd number is always an odd number.

Similarly, if $b$ is an odd number then $b^{2}$ will also be an odd number.

Thus, $a^{2} (odd number) = b^{2} (odd number) + c^{2}$

We know that sum of two odd numbers is always a even number.

So, $c^{2}$ must be an even number since $a^{2}$ is an odd number.

Therefore, for a right angle triangle with integer sides at least one of its measurements must be an even number because square of odd is odd and sum or difference of two odd is always even, so the third side automatically comes to be as even.

Andhra Pradesh Board Solutions for Chapter: Similar Triangles, Exercise 12: THINK - DISCUSS

Andhra Pradesh Board Mathematics Solutions for Exercise - Andhra Pradesh Board Solutions for Chapter: Similar Triangles, Exercise 12: THINK - DISCUSS

Questions from Andhra Pradesh Board Solutions for Chapter: Similar Triangles, Exercise 12: THINK - DISCUSS with Hints & Solutions

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