The perimeter of a right angled triangle is 4 times the shorter side. Find the ratio of other sides ??

• 4/5
  
  If sides of a right angles triangle are x, y & z with shorter side=x and longer side(hypotenuse)=z, then perimeter=x+y+z=4x or x=(y+z)/3 ---(i)
  Also y^2 + x^2= z^2 or z^2 - y^2= x^2 ---(ii)
  From (i), x^2=(y^2+2yz+z^2)/9, substituting this value in (ii), z^2 -y^2=(y^2 +2yz +z^2)/9 or
  10y^2 +2yz - 8z^2 =0
  Dividing above equation by z^2, we get 10(y/z)^2 +2(y/z) -8 =0
  By substituting y/z =a , 10a^2 +2a -8 =0 , 10a^2 +10a -8a -8 =0 ,(10a-8)(a+1)=0, so a=8/10=4/5
  So ratio of other sides=y/z=a=4/5
• 8 years agoHelpfull: Yes(1) No(0)