+0

# help

0
30
1

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

May 17, 2020

#1
+438
+3

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