Question 118436

given:

{{{y= -2x+5}}}

known: positions for the rectangular box defined by the {{{x}}} and {{{y}}} minimums and maximums

so, to find out what the dimensions of such a box are, first find midpoint coordinates of the line segment between {{{x-intecept}}} and {{{y-intecept}}} or
 between points 

{{{x[1]}}},{{{y[1]}}}= {{{2.5}}},{{{0}}} and 

{{{x[2]}}},{{{y[2]}}}= {{{0}}},{{{5}}}

That will be:

{{{x}}} coordinate of mid point is {{{(x[1] + x[2])/2 = (2.5 + 0)/2=1.25}}}

{{{y}}} coordinate of mid point is {{{(y[1] + y[2])/2 = (5 + 0)/2=2.5}}}
	
The mid point of segment joining two point is:

 ({{{1.25}}},{{{2.5}}})



Here is the graph that shows the point ({{{1.25}}},{{{2.5}}}):


*[invoke find_equation_of_line 1.25, 2.5, 0, 5]



the dimensions of a box are: {{{x =1.25}}} and {{{y = 2.5}}} 


its greatest possible area is:

{{{A = x*y }}}

{{{A = 1.25*2.5}}}

{{{A = 3.125}}}