Applying Pythagoras backwards (with minimal information)

Hello all!

While working on a personal project, I encountered the following math problem. I have a triangle with sides A, B, and C. I know the length of C = 15,3. Furthermore, I know that B / A = 7, so I can conclude that B = 7A. The triangle is a right angled triangle. To illustrate the problem, I have uploaded a visual representation attached to this post.

My goal is to know the lengths of sides A and B.

Is it possible to calculate those, and if so, how? It seems like a simple problem to solve with Pythagoras, but it's been years since I last touched any formulas. I've been breaking my head over it for the past few hours and just can't seem to get a (correct) answer. Do I need more information to calculate this? Any help would be greatly appreciated!

 

so, c^2=a^2+b^2

if given:
c = 15,3
b / a = 7=> b = 7a

we have

15.3^2=a^2+(7a)^2........solve for a
15.3^2=a^2+49a^2
15.3^2=50a^2
15.3^2/50=a^2
a=sqrt(15.3^2/50)
a=15.3/sqrt(50)
a=2.1637467504308354

b = 7a =>b = 7*2.1637467504308354=15.1462272530158478

exact solution:
a=2.1637467504308354
15.1462272530158478

we can round it to one decimal place, so sides a and b are:
a=2.2 and b=15.2

 

Very nice.

 

Thank you so much! This is a very clear explanation.

I tried replicating the process with some different C and B/A values to see if I understood what was happening, and now I consistently managed to solve the equation. Turns out I did something wrong squaring my combined A and B values previously, which messed up the formula. Much appreciated!

 

when doing that kind of problems, make sure to recognize what is hypothenuse, what are legs, and which one is to find
formula you need is: c^2=a^2+b^2 where c is hypothenuse, a and b are legs

it means


the biggest square has the exact same area as the other two squares put together





an example:



Let's check if the areas are the same:

3^2 + 4^2 = 5^2

Calculating this becomes:

9 + 16 = 25

25=25

 

This is a math professional reply. A job well-done!