It will take 210 ft of fencing to enclose a rectangular play

It will take 210 ft of fencing to enclose a rectangular playground with an area of 2700 square feet. Find the dimensions of the playground. Find length and width.

Solution

Let x be length and y be width.

Lenght of fencing = perimeter of field

2x+2y = 210 ----(1)

x*y = 2700 ----(2)

Solve the two equations to get x and y:

y = 2700/x .Substitute in equation 1

2x+ 2(2700/x) = 2700

x+ 2700/x = 1350

x^2 -1350x +2700 =0

Solve the quadratic equation: x = 675 + 673, 675 -673

x = 1348 , 2

y = 2700/1348 , 2700/2 = 2, 1350

Solution : (lenght , width) ---( 1348ft , 2ft) and ( 2 ft, 1350ft )