# Thread: Solving Pythagoras Theorem eqn a^2 + (1.3a)^2 = c^2 for "a": possible?

1. ## Solving Pythagoras Theorem eqn a^2 + (1.3a)^2 = c^2 for "a": possible?

I thought I remembered my algebra from a half century ago. I don't.
Is it possible to solve the equation below for a? <--- CORRECTION: initial post said "c" here. That was a mistake. I meant "a"
a^2 + (1.3a)^2 = c^2
Why? Because I'm trying to constrain (crop) an image to have a certain number of pixels. 1.3 is the image's aspect ratio. So the Pythagorean b is equal to 1.3a

So the above is the
Pythagorean formula:
Width^2 * (1.3 * Width)^2 = Total_Pixels^2
TIA

2. Originally Posted by tfield98
I thought I remembered my algebra from a half century ago. I don't.
Is it possible to solve the equation below for c?
a^2 + (1.3a)^2 = c^2
Why? Because I'm trying to constrain (crop) an image to have a certain number of pixels. 1.3 is the image's aspect ratio. So the Pythagorean b is equal to 1.3a

So the above is this Pythagorean formula:

Width^2 * (1.3 * Width)^2 = Total_Pixels^2
TIA
You'll need a square root.

3. Originally Posted by tkhunny
You'll need a square root.
Thanks, tkhunny.

My mistake, I meant to say "solve for a, knowing c"

4. Originally Posted by tfield98
a^2 + (1.3a)^2 = c^2
solve for a, knowing c
Let k = 1.3; then:

a^2 + (ka)^2 = c^2
a^2 + k^2 * a^2 = c^2
a^2(1 + k^2) = c^2
a^2 = c^2 / (1 + k^2)
a = sqrt[c^2 / (1 + k^2)]

Try that out using (as example) k = 3 and c^2 = 250
You'll get a = 5

Now that you're satisfied(!), use it on your problem

5. ## Solving Pythagoras Theorem eqn a^2 + (1.3a)^2 = c^2 for "a": possible?

Originally Posted by Denis
Let k = 1.3; then:

a^2 + (ka)^2 = c^2
a^2 + k^2 * a^2 = c^2
a^2(1 + k^2) = c^2
a^2 = c^2 / (1 + k^2)
a = sqrt[c^2 / (1 + k^2)]
That's exactly what I was looking for. Thanks!!

The algebra is straight-forward, but I couldn't have come up with it on my own.