a rectangular garden covers 46yd. The length is 3 yd longer than the with. Find the length and with.

Question

a rectangular garden covers 46yd. The length is 3 yd longer than the with. Find the length and with.

Answer 1

Need area units, 46 yd²

 

1)  A = L*W = 46 yd²     (A = area of garden   L = length of garden   W = widths of garden

 

2)  L = W + 3                Substitute for L in equation 1)

  

   A = (W + 3)*W = W² + 3*W = 46        (rearrange to quadratic equation  a*x² + b*x + c = 0)

 

  W² + 3*W - 46 = 0                  (solve quadratic)    x = [-b ±√(b² - 4*a*c)]/2*a      a = 1   b = 3    c = -46

 

 

W = [-3 + √(3² + 4*1*46)]/2*1 = [-3 + √(9 + 184)]/2 = [ -3 + 13.892]/2 = 5.446 yd       (only positive root)

 

L = A/W = 46/5.446 = 8.446 yd