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)
Answer This Question
Related Questions
 Combinatorics (math)  In a certain country, 40 roads lead out of each city. ...
 Poetry/English  I am STILL trying to find 3 poetic devices in the poem "The ...
 The road not taken last question  for my last question How do you think the ...
 Poem: The road not taken by Robert Frost  Could you check these answers thanks...
 maths geometry  A straight road separates towns A (grid ref 42,45) and B (grid ...
 math trigonometry  1. Two straight roads intersect to form an angle of 75". ...
 author  Which of the following, if true, provides the strongest support for an ...
 Math  One road has a grade of 20% and the other has an elevation of 15 degrees...
 Math  How do i figure out this question? There are two roads, one has a grade ...
 Language Arts  In "The Road Not Taken" when Frost says two roads"....that ...
More Related Questions