Question

Find the maximum area of a rectangle whose perimeter is 100m.

Answer 1

Step-by-step explanation:

100=x+x

then,

100=2x

x=100/2

x=50 is length of rectangle

100=50+x

x=100-50

x=50 is the rectangle breaths

Answer 2

The maximum area is 625 meters square.

GIVEN

The perimeter of a rectangle - is 100 meters.

TO FIND:

Area of the rectangle.

SOLUTION:

We can simply solve the given problem as under.

Let, the length of the rectangle be, l

the and width of the rectangle be B

we know that the,

the perimeter of a rectangle twice the sum of its length and width.

so, 2(L+w) = 100

L+w = 50

w = 50-L

The Area of a rectangle is the product of it

's length and width.

Let the maximum area be, a.

so, L × w = A

putting the value of w from equation (I) in (II) we have,

L(50-L) = A

The first derivative gives;

$\frac{da}{dl} = 50 - 2 \times l \: = \frac{da}{dl} = 0 = l = 25$

Hence, For W=L = 25 We Have The Maximum Area Which Is;

a = l × w

a = 625

HENCE the maximum area is 625 meters square.

#Spj3

For more such question-

https://brainly.in/question/14934223?utm_source=android&utm_medium=share&utm_campaign=question

https://brainly.in/question/12753130?utm_source=android&utm_medium=share&utm_campaign=question