Question 258855
The formula for the sides of a triangle is {{{A^2 + B^2 = C^2}}} Where C is the hypotenuse.

In your case the two sides have a ratio to each other that is equal to 16:9 so we will modify the equation a little.

The new equation:{{{(16*X)^2 + (9*X)^2 = C^2}}}
Now we know that C = 50
{{{(16*X)^2 + (9*X)^2 = 50^2}}}
Now we can simplify this equation by squaring the terms
{{{256*X^2 + 81*X^2 = 2500}}}
The left side can be rewritten by dividing X^2 out of it
{{{X^2 * (256 + 81) = 2500}}}
Simplify
{{{X^2 * (337) = 2500}}}
Divide both sides by 337
{{{X^2 = 7.418}}} Note that from here on out I will be rounding so the numbers may not be exact
Then take the square root of both sides
{{{X = 2.724}}}

Now we have to go back to the ratio that was given at the start of the problem
16:9
A = 16 * 2.724
{{{highlight(A = 43.58)}}}
B = 9 * 2.724
{{{highlight(B = 24.52)}}}

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Checking the answers
Plug the calculated values back into the triagle equation
{{{A^2 + B^2 = C^2}}}
{{{43.58^2 + 24.52^2 = 50^2}}}
{{{1899.22 + 601.23 = 2500}}}
{{{2500.45 = 2500}}} Notice the answer is off slightly due to rounding