The dimensions for this rectangle are b= 30 ft and h=20 ft.
<h3>Perimeter</h3>The perimeter of a geometric figure is the sum of its sides.
The question gives:
- the geometric figure - rectangle
- the total perimeter - 120 ft
Therefore for the perimeter, you have
P= + h+ h +h
P=2b+3h
2b+3h=120 (1)
From equation 1, you can write:
2b=120-3h
b=
b= 60 - (2)
The area for the rectangle is given by A= bh. Therefore, by replacing (2) in the formula for rectangle area, you have:
The maximum area will be calculated from the derivation of the previous equation of area.
The maximum area can be found when the first derivative is equal to zero. Thus,
60-3h=0
-3h=-60 *(-1)
3h=60
h=20
Now, you know the height and from equation 2 (b= 60 - ) you can find the base.
b= 60 -
b=60 - 3*10
b=60-30
b=30
Read more about the First Derivative Test here:
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