Question 122350
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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^2+b^2=c^2}}} and recognizing that a = x, b = 2x, and c = 21 we can write:


{{{x^2+(2x)^2=441}}}


{{{x^2+4x^2=441}}}


{{{5x^2=441}}}


{{{x^2=441/5}}}


{{{x=sqrt(441/5)=sqrt(441)/sqrt(5)=21/sqrt(5)}}}


Lastly, rationalize the denominator:


{{{x=(21/sqrt(5))*(sqrt(5)/sqrt(5))=(21*sqrt(5))/5}}}


Which gives us an expression for the short side.


The long side is twice that, so


Long side = {{{2x=(42*sqrt(5))/5}}}


I'll leave the calculator work to you.

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