First, to make it easier to work with the numbers let's convert each mixed number to an improper fraction:
#38 1/4 = 38 + 1/4 = (4/4 xx 38) + 1/4 = 152/4 + 1/4 = (152 + 1)/4#
#= 153/4#
#4 1/2 = 4 + 1/2 = (2/2 xx 4) + 1/2 = 8/2 + 1/2 = (8 + 1)/2 = 9/2#
The formula for the area of a rectangle is:
#A = l xx w#
We can now substitute and solve for #l#:
#153/4 = l xx 9/2#
#153/4 xx color(red)(2)/color(blue)(9) = l xx 9/2 xx color(red)(2)/color(blue)(9)#
#(color(blue)(cancel(color(black)(153)))17)/(color(red)(cancel(color(black)(4)))2) xx cancel(color(red)(2))/cancel(color(blue)(9)) = l xx color(blue)(cancel(color(black)(9)))/color(red)(cancel(color(black)(2))) xx cancel(color(red)(2))/cancel(color(blue)(9))#
#17/2 = l#
#l = 17/2#
We can now convert this to a mixed number:
#17/2 = (16 + 1)/2 = 16/2 + 1/2 = 8 + 1/2 = 8 1/2#
The length of the garden is #8 1/2# meters
