SOLUTION: a triangle has a hypotenuse of 50 the other sides of the triangle have the ratio of 16:9 what are the lengths of the sides of the triangle

Algebra ->  Pythagorean-theorem -> SOLUTION: a triangle has a hypotenuse of 50 the other sides of the triangle have the ratio of 16:9 what are the lengths of the sides of the triangle      Log On


   

Question 258855: a triangle has a hypotenuse of 50
the other sides of the triangle have the ratio of 16:9
what are the lengths of the sides of the triangle
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the sides of a triangle is A%5E2+%2B+B%5E2+=+C%5E2 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:%2816%2AX%29%5E2+%2B+%289%2AX%29%5E2+=+C%5E2
Now we know that C = 50
%2816%2AX%29%5E2+%2B+%289%2AX%29%5E2+=+50%5E2
Now we can simplify this equation by squaring the terms
256%2AX%5E2+%2B+81%2AX%5E2+=+2500
The left side can be rewritten by dividing X^2 out of it
X%5E2+%2A+%28256+%2B+81%29+=+2500
Simplify
X%5E2+%2A+%28337%29+=+2500
Divide both sides by 337
X%5E2+=+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%28A+=+43.58%29
B = 9 * 2.724
highlight%28B+=+24.52%29
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Checking the answers
Plug the calculated values back into the triagle equation
A%5E2+%2B+B%5E2+=+C%5E2
43.58%5E2+%2B+24.52%5E2+=+50%5E2
1899.22+%2B+601.23+=+2500
2500.45+=+2500 Notice the answer is off slightly due to rounding