Answer:
[tex]c=b\sqrt{2}[/tex]
Step-by-step explanation:
Refer to the attached image.
A right triangle is considered so when one of its corners are 90°.
If sides a and b are equal in length, then the corners across from them are equal in size as well.
The only way for this to be possible is if both corners A and B(opposite of sides a and b) are 45°.
Pythagorean theorem
This theorem states that the square of a right triangle's long side is equal to the sum of the squares of the shorter sides.
In this case:
[tex]a^{2} +b^{2} =c^{2}[/tex]
but since:
[tex]a=b[/tex]
the equation can be solved by replacing a with b in the equation:
[tex]b^{2} +b^{2} =c^{2} \\2b^{2}=c^{2} \\\sqrt{2b^{2} } = c\\b\sqrt{2} =c[/tex]
