Solving for Unknown Sides in a Right Triangle: Pythagorean Theory Help

[christian0710]

Hi
if i have a diagonal in a right triangle costing of 4x and let's say the two sides are a (same size).

Is it then correct to write (4r)²=2a² or is it correct to write
4r²=2a²

If (4r)²=2a² is correct, is it then correct to say 16r²=2a² and √(2a²)/16)

 

[Mentallic]

I'm really confused with what you're asking. Start again, and slowly, explain what the length of each side is.

 

[HallsofIvy]

Hi
if i have a diagonal in a right triangle costing of 4x and let's say the two sides are a (same size).

What does "consisting of 4x" mean?

Is it then correct to write (4r)²=2a² or is it correct to write
4r²=2a²

Where did "r" come from? Is it what you called "x" before?

IF the length of the diagonal is 4r and the two sides have length a, then the Pythagorean theorem says that $(4r)^2= a^2+ a^2$ or $(4r)^2= 2a^2$.

If (4r)²=2a² is correct, is it then correct to say 16r²=2a² and √(2a²)/16)

Yes, $(4r)^2= 16r^2= 2a^2$. I don't know what that last expression is supposed to be but if $16a^2= 2a^2$ then $r^2= 2a^2/16= a^2/8$ and, taking square roots of both sides, $r= a/\sqrt{8}= a/(2\sqrt{2})= a\sqrt{2}/4$.