A rectangular lawn measuring 10 by 8 is surrounded by a path of uniform width x meteres. If the are of the path is 60m what is x?
+129839 The border of x adds 2x to each dimension of the 8 x 10 rectangle....and we have.....
L * W = original area + added area
(10 + 2x) (8 + 2x) = 10*8 + 60
80 + 16x + 20x + 4x^2 = 80 + 60
4x^2 + 36x + 80 = 80 + 60
4x^2 + 36x = 60
4x^2 + 36x - 60 = 0 divide by 4
x^2 + 9x - 15 = 0
Using the quad formula, x = [ √141 - 9 ] / 2 ≈ 1.4372 m
