Math
posted by Ashley .
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
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 = Â±11/13
We know we need a negative slope, so m = 11/13
The minimum area is thus 7150 
Math 
Steve
oops on typos
That should be 1/2 (5565m)(6555/m)
Respond to this Question
Similar Questions

maths geometry
A straight road separates towns A (grid ref 42,45) and B (grid ref 52,40) A village is situated at grid ref (46,57) and a new road is planned from the village to road AB. What is the shortest road possible (1 dp) Please define an origin … 
The road not taken last question
for my last question How do you think the different roads in these peoms might symbolize or reperensent the situations of the two speakers? 
Poem: The road not taken by Robert Frost
Could you check these answers thanks. 1. Where do Frost's roads diverge? 
author
Which of the following, if true, provides the strongest support for an archaeologistâ€™s conclusion that a particular stretch of ancient stonepaved road was part of the Inca road system? 
Poetry/English
I am STILL trying to find 3 poetic devices in the poem "The Road Not Taken" by Robert Frost: Please advise if I am on the "right road" or could you put me on "the right path if I am wrong... line 12 "In leaves no step had trodden black"is … 
Math
One road has a grade of 20% and the other has an elevation of 15 degrees. Which road would be steeper? 
math trigonometry
1. Two straight roads intersect to form an angle of 75". Find the shortest distance from one road to a gas station on the other road 10o0 m from the junction. 2. Two buildings with flat roofs are 60 m apart. From the roof of the shorter … 
Combinatorics (math)
In a certain country, 40 roads lead out of each city. When all roads are open, it is possible to travel from any city to any other. Each road leads from one city to another; there are no dead end roads. If one road is closed for repairs, … 
math trigonometry
two straight roads intersect to form an angle of 75 degree. find the shortest distance from one road to a gas station on the other road 1000 m from the junction. 
math
Two motorcycles are at the two ends of a road right next to a wall behind them (walls and road are perpendicular. They start heading towards one another in the opposite directions on two straight and parallel lines.Each vehicle has …