For what value of a is there a right triangle with sides a + 1, 6a and 6a + 1?
+738 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!
:)
