SOLUTION: if the hypotenuse of a right angled triangle is 3 root 10.the smaller side is tripled and longer side is doubled the new hypotenuse is 9 root 5. find the length of the side

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Question 734636: if the
hypotenuse of a right angled
triangle is 3 root 10.the
smaller side is tripled and
longer side is doubled the new
hypotenuse is 9 root 5. find the
length of the side
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the smaller side
y= length of the longer side

Applying the Pythagorean theorem:
x%5E2%2By%5E2=%283sqrt%2810%29%29%5E2 --> x%5E2%2By%5E2=3%5E2%2A%28sqrt%2810%29%29%5E2 --> x%5E2%2By%5E2=9%2A10 --> x%5E2%2By%5E2=90

3x= length of the tripled smaller side
2y= length of the doubled longer side

Applying the Pythagorean theorem:
%283x%29%5E2%2B%282y%29%5E2=%289sqrt%285%29%29%5E2 --> 9x%5E2%2B4y%5E2=9%5E2%2A%28sqrt%285%29%29%5E2 --> 9x%5E2%2B4y%5E2=81%2A5 --> 9x%5E2%2B4y%5E2=405

Now, we have the system of equations (linear in x%5E2 and y%5E2)
system%28x%5E2%2By%5E2=90%2C9x%5E2%2B4y%5E2=405%29
which can be easily solved to find
x%5E2=9 and y%5E2=81, so highlight%28x=3%29 and highlight%28y=9%29