(6) A garden is 300 metres wide and 400 metres long. There is a pathway that runs along the perimeter inside the garden. The area of the pathway is half of the area of the park. What is the width of the pathway?
Let x be the width of the pathway......then.....we have an inner rectangle whose area is defined as:
(300 - 2x) (400 - 2x) = 60,000m^2 simplify
120000 - 1400x + 4x^2 = 60000 subtract 60000 from each side
4x^2 - 1400x + 60000 = 0
x^2 - 350x + 15000 = 0 ........factor
(x - 50) (x - 300) = 0 setting each factor to 0, x= 300m (reject) or x = 50m......which is correct
