Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 244 meters

1 answer:

6 0

We know that

[perimeter of rectangle]=2*(length+width)

Let
x-----------> length
y-----------> width
so
P=2*(x+y)-----------> 244=2*(x+y)-----> x+y=122-------> y=122-x

Area=x*y-------> x*(122-x)----> 122x-x²

find the derivative function and equals to zero

122-2x=0-----> 122=2x----------> x=61 m
y=122-x------> y=122-61---------> y=61 m

the maximum area is given by a square

the answer is
is a square of side 61 m

You might be interested in

A water hose had filled up 1⁄3 of a pool after 1⁄2 of an hour. At this rate, how many hours would it take to fill the pool?

Vlad1618 [11]

$\huge{ \rm{Question:}}$

A water hose had filled up 1⁄3 of a pool after 1⁄2 of an hour. At this rate, how many hours would it take to fill the pool?

$\huge{ \rm{Answer:}}$

It takes 1.5 hours or 1 hour and 30 min. to fill the pool.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The commission of selling each iPhone is $30 and the commission of selling each iPad is $20. If you one day sold 4 more iPhones

sineoko [7]

lets assume number of iphones sold = a number of ipads sold = b i sold 4 iphones more than ipad that becomes a = b+4 then the equation of total commission becomes 30a+20b = 520 substituting a =b+4 in the above equation 30(b+4)+20b = 520 30b+120+20b = 520 50b =520-120 50b = 400 b = 400/50 b=8 number of iphones i sold = a = b+4 = 8+4 = 12 number of ipads i sold = 8 so i sold 12 iphones and 8 ipads to earn the commission of $520

4 0

3 years ago

Which equation best represents this situation? The number 88 is equal to a number divided by 11. A. 88 = 11g B. 88 = 11 + g C. 8

miv72 [106K]

The answer is D. 88=g/11

4 0

3 years ago

Read 2 more answers

The width of a rectangle is 8y- 1.5 feet and the length is 1.5y+9 feet. Find the perimeter of the rectangle.

lyudmila [28]

Answer:

$P=19y+15$