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For what value of a is there a right triangle with sides a + 1, 6a and 6a + 1?

 May 17, 2020
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Hi Guest!
 

This is a right triangle, so the hypotenuse would be \(6a+1\) since the hypotenuse is the longest side.

 

So, \((a+1)^2+(6a)^2=(6a+1)^2\).

 

\(a^2+2a+1+36a^2=36a^2+12a+1\)

\(a^2+2a=12a\)

\(a^2=10a\)

 

So, \(a=0, \text{ or } a=10\)

 

But, a length cannot be 0, so \(\boxed{a=10}!\)

 

I hope this helped you, guest!
:)

 May 17, 2020

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