Q. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saves a distance equal to half the longer side. Then find the ratio of the shorter side to the longer side.

• ratio of sides =3/4
  
  if sides are 3x and 4x
  
  distance while walking on side = 3x+4x=7x
  distance on diagonal = 5x
  distance saved = 2x which is half of 4x.
• 12 years agoHelpfull: Yes(18) No(3)
• l+b-1/2l=1/2*sqrt(l^2+b^2)(diagonal in a right angled triangle)
  2*(l+b-1/2l)=sqrt(l^2+b^2)
  (l+2b)^2=l^2+b^2
  l^2+4*b^2+4*l*b=l^2+b^2
  3b^2=-4lb
  -3b=4l
  b/l=4/-3
• 12 years agoHelpfull: Yes(1) No(1)
• Let length be x and breadth be y.
  Length of diagonal== sqrt./```````(x^2 +y^2)
  According to question
  
  sqrt.(x^2+y^2)==(x+y)-x/2.
  Squaring both equation
  x^2 + y^2 == x^2 +y^2 + 2xy +x^2/4 - 2 * (x+y) *x/2
  2(x+y)x/2== 2xy+x^2/4
  x^2 +xy == 2xy +x^2/4
  3 x^2/4 == xy
  3/4*x=y
  3/4=y/x; Answer Ratio between shorter to longer is 3:4
• 6 years agoHelpfull: Yes(1) No(0)
• Lets consider shorter side length= x, and longer side length= l;
  
  then the original route=x+l;
  
  short cut is = (x+l)-(l/2) ;
  
  diagonal= sq. root of (x^(2)+l^(2))
  
  Equating diagonal and short cut length,
  
  sq.root(x^(2)+l^(2))=(x-l/2);
  On simplification,
  
  we get, x:l= 3:8 ;
• 7 years agoHelpfull: Yes(0) No(1)