Question 936034

If we have a {{{90}}}° triangle and one of the sides is {{{a=20x}}} and the other is {{{b=9x}}} find the  hypotenuse.

The area is 

{{{720cm^2=(1/2)a*b}}}

{{{720cm^2=(1/2)20x*9x}}}

{{{720cm^2=10x*9x}}}

{{{720cm^2=90x^2}}}

{{{720cm^2/90=x^2}}}

{{{72cm^2/9=x^2}}}

{{{8cm^2=x^2}}}

{{{x=sqrt(8cm^2)}}}

{{{x=2.82842712474619cm}}}


the  hypotenuse {{{c^2=a^2+b^2}}}

{{{c^2=(20x)^2+(9x)^2}}}

{{{c=sqrt(400x^2+81x^2)}}}

{{{c=sqrt(481x^2)}}}

{{{c=21.93171219946131x}}}

{{{c=21.93171219946131*2.82842712474619cm}}}

{{{c=62.03224967708329cm}}}


{{{a=20*2.82842712474619cm}}}

{{{a=56.5685424949238cm}}}

{{{b=9*2.82842712474619cm}}}

{{{b=25.45584412271571cm}}}


check:

{{{c^2=a^2+b^2}}}

{{{(62.03224967708329cm)^2=(56.5685424949238cm)^2+(25.45584412271571cm)^2}}}

{{{3848cm^2=3200cm^2+648cm^2}}}

{{{3848cm^2=3848cm^2}}}


{{{720cm^2=(1/2)a*b}}}

{{{720cm^2=(1/2)56.5685424949238cm*25.45584412271571cm}}}

{{{720cm^2=(1/2)1440cm^2}}}

{{{720cm^2=720cm^2}}}

ps: only if you use all decimal places you can get exact result