A rectangular field is 16m long and 10m wide . there is a path of uniform width all around it having an area of 120 m² .find the width of the path
+128475 We have four squares with sides of w , two rectangles of 10w and two rectangles of 16w
So...we have
4w^2 + 2( 10w) + 2(16w) = 120
4w^2 + 20w + 32w = 120
4w^2 + 52w = 120 divide through by 4
w^2 + 13w = 30 rearrange as
w^2 + 13w - 30 = 0 factor as
(w + 15) ( w - 2) = 0
The second factor set to 0 is what we need
w - 2 = 0
w = 2 ft = width of the path
