The hypotenuse of a right angled triangle is 6 m more than twice then shortest side. The third side is 2 m less than the hypotenuse.
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let h be the hypotenuse
By Pythogoras theorem
shortest side is √h^2-(h-2)^2=√2(2h+2)=√4(h+1)=2√(h+1)
h=4√(h+1)+6
h-6=4√(h+1)
squaring both sides
h^2-12h+36= 16h+16
⇒h^2-28h+20=0
which gives h
By Pythogoras theorem
shortest side is √h^2-(h-2)^2=√2(2h+2)=√4(h+1)=2√(h+1)
h=4√(h+1)+6
h-6=4√(h+1)
squaring both sides
h^2-12h+36= 16h+16
⇒h^2-28h+20=0
which gives h
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