Question 118436: A rectangular box is to be placed in the first quadrant in such a way that one side lies on the positive x-axis and one side lies on the positive y-axis. The box is to lie below the line y=-2x+5. Give the dimensions of such a box having greatest possible area.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
given:
known: positions for the rectangular box defined by the  and  minimums and maximums
so, to find out what the dimensions of such a box are, first find midpoint coordinates of the line segment between  and  or
between points
 , =  , and
 , = ,
That will be:
coordinate of mid point is 
coordinate of mid point is 
The mid point of segment joining two point is:
( ,)
Here is the graph that shows the point (,):
| Solved by pluggable solver: FIND EQUATION of straight line given 2 points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1.25, 2.5) and (x2, y2) = (0, 5).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is  , or  .
y=(-2)x + (5)
Your graph:
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the dimensions of a box are:  and 
its greatest possible area is:
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