anonymous
  • anonymous
the hypotenuse of a right triangle is 3m more than twice the short leg. the longer leg is 2m more than twice the shorter leg. find the lengths of the sides?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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myininaya
  • myininaya
s=short leg h=hypotenuse l=other leg h=3+2s l=2+2s right triangle use Pythagorean thm so h^2=l^2+s^2 (3+2s)^2=(2+2s)^2+s^2 solve for s
myininaya
  • myininaya
9+2*3*2s+4s^2=4+2*2*2s+4s^2+s^2 9+12s+4s^2=4+8s+4s^2+s^2 4s^2-4s^2-s^2+12s-8s+9-4=0 -s^2+4s+5=0 s^2-4s-5=0 (s-5)(s+1)=0 s=5 s=-1
myininaya
  • myininaya
but a leg cannot have length -1 so s=5 is the shorter leg if s=5, then h=3+2(5)=13 and l=2+2(5)=12 we can check h^2=s^2+l^2 does it? 13^2=5^2+12^2 169=25+144 169=169 so done! everything checks out!

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anonymous
  • anonymous
thank you lots =]

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