Find the dimensions of a rectangle with perimeter 100 m whose area is as large a

jeliceg2

jeliceg2

Answered question

2021-11-17

Find the measurements of a rectangle with a 100 m perimeter and the largest possible area.

Answer & Explanation

Nicole Keller

Nicole Keller

Beginner2021-11-18Added 14 answers

Let the lehgth be x and width be y
Then we can write
Perimeter =2(x+y)
100=2(x+y)
Divide both sides by 2
50=x+y
50x=y
Area=xy
A(x)=x(50x)
A(x)=50xx2
DIfferentiate
A(x)=502x
Solve the equation A(x)=0
502x=0
Add 2x on both sides
50=2x
Divide both sides by 2
25=x
Substitute x=25 in Equation 1, to get
5025=y
25=y
So the rectangle with maximum area is a square with side length 25 m
Result: Rectangle with maximum area is a square with side length 25 m.

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