The width of a rectangular garden is 20cm less than twice the length. The perimeter is at least 52 cm. Find the minimum dimensions, in feet, if each dimension is an integer.

Question

The width of a rectangular garden is 20cm less than twice the length. The perimeter is at least 52 cm. Find the minimum dimensions, in feet, if each dimension is an integer.

Answer 1

W=2L-20, 2L= W+20

P=2L+2W = W+20+2W = 3W + 20 > 52

W > 32/3 = 10 2/3 cm

L> 32/6+10 = 92/6 = 15 1/3 cm

2.54 cm = 1 inch = (1/12) foot

(32/3)/2.54 = X/(1/12)

X = (1/12)(32/3)/2.54 = (1/3)(8/3)/2.54 = (8/9)/2.54= 8/(9)(2.54) minimum feet for width

Y=(1/12)(92/6)/2.54 =(1/3)(23/6)/2.54 =(23/18)/2.54 = 23/(18)(2.54) = minimum feet for length