SOLUTION: Christine has a solar panel with a width of 21 in. To get the proper inclination for her climate, she needs a right triangle support frame that has one leg twice as long as the oth

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Question 122350: Christine has a solar panel with a width of 21 in. To get the proper inclination for her climate, she needs a right triangle support frame that has one leg twice as long as the other. To the nearest tenth of an inch, what dimensions should the frame have?
Hint: Do not round your answer(s) until the very end.
Shorter side=?
Longer side=?
Found 3 solutions by solver91311, checkley71, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Let's say the short leg measures x inches.  Then the long leg must measure
2x inches, and the hypotenuse of the triangle is 21 inches, or the width of
the solar panel.


Using Pythagoras: a%5E2%2Bb%5E2=c%5E2 and recognizing that a = x, b = 2x, and c = 21 we can write:


x%5E2%2B%282x%29%5E2=441


x%5E2%2B4x%5E2=441


5x%5E2=441


x%5E2=441%2F5


x=sqrt%28441%2F5%29=sqrt%28441%29%2Fsqrt%285%29=21%2Fsqrt%285%29


Lastly, rationalize the denominator:


x=%2821%2Fsqrt%285%29%29%2A%28sqrt%285%29%2Fsqrt%285%29%29=%2821%2Asqrt%285%29%29%2F5


Which gives us an expression for the short side.


The long side is twice that, so


Long side = 2x=%2842%2Asqrt%285%29%29%2F5


I'll leave the calculator work to you.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
ASSUMING THE 21 INCHES IS THE HYPOTENUSE.
X^2+(2X)^2=21^2
X^2+4X^2=21^2
5X^2=441
X^2=441/5
X^2=88.2
X=SQRT88.2
X=9.3915 INCHES FOR THE SHORT LEG.
2X=2*9.3915=18.783 INCHES FOR THE LONG LEG.
PROOF
9.3915^2+18.783^2=21^2
88.2+352.8=441
441=441

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Christine has a solar panel with a width of 21 in. To get the proper inclination for her climate, she needs a right triangle support frame that has one leg twice as long as the other. To the nearest tenth of an inch, what dimensions should the frame have?
Hint: Do not round your answer(s) until the very end.
---------------
Let one of the legs be "x" inches; Then the other leg is "2x" inches.
x^2 + (2x)^2 = 21^2
x^2+4x^2= 21^2
5x^2 = 21^2
x^2 = 441/5
x^2 = 88.2
x = 9.3915
---------------
Shorter side=9.3915 inches
Longer side= 18.783 inches
=============================
Cheers,
Stan H.