there is a rectangulaq park of area 1500 sq m. The sum of its diagonal and length is 5 times its breadth. What is the breadth of the park

• let breadth= b
  length= a
  given
  a*b=1500 & (a^2 +b^2)^1/2 + a= 5b
  now
  (a+b)^2= a^2 + b^2+ 2ab
  = a^2+ b^2+3000
  so, a^2+b^2= (a + b)^2-3000
  sqare root both sides
  {(a^2+b^2)}^1/2= [(a+b)^2-3000]^1/2= (5b-a)
  so,
  (a+b)^2 - 3000=(5b-a)^2
  a^2 + b^2 + 2ab-3000 = 25 b^2+ a^2-10ab .....and v know.......... ab=1500
  on solving
  24 b^2 -18000+3000=0
  hence breadth= 25 mtrs ................answer
  and length= 60 mtrs
  proof:
  diagonal+leangth= (25*25 + 60*60)^1/2 + 60 = 5*25
• 11 years agoHelpfull: Yes(0) No(0)