# Each side of the triangle ABC was increased by 1. Could the resulting triangle be rectangular again?

September 29, 2021 | education

| Let’s say that we increased each side by 1 then according to the law of Pythagoras. We should get the following expression:

(c + 1) ^ 2 = (a + 1) ^ 2 + (b + 1) ^ 2.

Let’s expand the brackets:

c ^ 2 + 1 = a ^ 2 +1+ b ^ 2 + 1.

c ^ 2 + 1 = a ^ 2 + b ^ 2 + 2

As you can see, the equation cannot be correct since 1 does not equal 2.

This means that such a triangle will not be rectangular.

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