Posted by Ashley on Tuesday, January 29, 2013 at 11:52am.
Two roads intersect at right angles. A water spring is located 65 m from one road and 55 m from the other road. A straight path is to be laid out to pass the spring from one road to the other. Find the least area that can be bounded by the roads and the path.
area in m2 =
can anyone shed some light on this questions....

Math  Steve, Tuesday, January 29, 2013 at 12:37pm
Basically you want the smallest area bounded by the x and yaxes, and any line passing through (65,55).
A line through (65,55) with slope m will have intercepts at y = 5565m and x=65+55/m
So, the area of the enclosed triangle is
a(m) = 1/2 (55+65m)(65+55/m)
a(m) = 25/2m (1113m)^2
da/dm = 25/2 (121/m^2  169)
da/dm=0 when m = ±11/13
We know we need a negative slope, so m = 11/13
The minimum area is thus 7150 
Math  Steve, Tuesday, January 29, 2013 at 12:37pm
oops on typos
That should be 1/2 (5565m)(6555/m)