SOLUTION: 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 th

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:

the dimensions of a box are: and

its greatest possible area is:

RELATED QUESTIONS
A regular hexagon of side length 2a is placed so that the center is at the origin, and... (answered by Alan3354)

a box has a rectangular base of 30cm by 25cm iron rods are to be placed in the box... (answered by ewatrrr)

A rectangle has one vertex in quadrant 1 on the graph of y=16-x^2, another at the origin, (answered by Fombitz)

A rectangle has one vertex in quadrant I on the graph of y=10-x^2, another at the origin, (answered by TimothyLamb,KMST)

Identify the quadrant or axis that the following point lies on. If the point lies on an... (answered by ikleyn,Alan3354)

Find cos(z) and sin(z) if z is an angle in quadrant III (in standard position) and the... (answered by jim_thompson5910)

Hi, I could really use some help with this problem. A rectangle has one vertex on the... (answered by scott8148)

Overlay a rectangular coordinate system on a Little League baseball diamond so that the... (answered by textot)

Find the dimensions and the area of the largest rectangle that can be fit under the graph (answered by MathLover1,greenestamps)