If the side of the garden parallel to the building has length x meters, express the amount of fencing needed as a function of x

Question

A rectangular garden with an area of 250 square meters is to be located next to a building and fenced on three sides, with the building acting as a fence on the fourth side

Answer 1

Area = length* width

 

250 = x * width

 

width = 250/x

 

Perimeter = 2 x length + 2 x width

 

              =  2X + 2(250/x)

 

             = 2X + 500/x =    (2x^2 + 500)/X = P(x)

 

CHECK:

   Let length x = 25. Then width is 250/25 = 10.

   THe perimeter is then 2 * (25+10) = 2*(35) = 70

 

   p(25) = (2*25*25+500)/25 = (1250+500)/25 = 1750 / 25 = 70 <--- YES!!!