the perimeter of a rectangle is 40m.if the sides of the rectangle are natural noumber find the dimensions of the rectangle having the maximum area
Answers
Answer:
Your gut feeling may tell you it's a square, with sides 10 ft, or a total area of 100 sqft.
Explanation:
You can divert from this and see if the area gets any larger, or you can use the mathematical way:
If the length =
x
and the width =
y
then the perimeter
P
=
40
P
=2x+2y
=40→x+y
=20→y
=20−x
As for the area A :A=x⋅y
=x.(20−x)
=20x−x2
And we have to find an extreme for that:
We can do this by setting the derivative to
=0
A
'
=20−2x
=0→x
=10→y
=10
Just as we thought in the first place.
graph{20x-x^2 [-131.6, 135.4, -8.4, 125.1]}
hope it help you
plz mark it
Answer:
Your gut feeling may tell you it's a square, with sides 10 ft, or a total area of 100 sqft.
Explanation:
You can divert from this and see if the area gets any larger, or you can use the mathematical way:
If the length =
x
and the width =
y
then the perimeter
P
=
40
P
=2x+2y
=40→x+y
=20→y
=20−x
As for the area A :A=x⋅y
=x.(20−x)
=20x−x2
And we have to find an extreme for that:
We can do this by setting the derivative to
=0
A
'
=20−2x
=0→x
=10→y
=10
Just as we thought in the first place.
graph{20x-x^2 [-131.6, 135.4, -8.4, 125.1]}
hope it help you
Step-by-step explanation: