SOLUTION: The perimeter of a rectangle is 24cm Which of the following could not be the area of the rectangle. Please explain A. 40 cm2 B. 11 cm2 C. 27 cm2 D. 32 cm2 E. 20 cm2 Regar

Question 1142910: The perimeter of a rectangle is 24cm
Which of the following could not be the area of the rectangle. Please explain
A. 40 cm2
B. 11 cm2
C. 27 cm2
D. 32 cm2
E. 20 cm2
Regards

Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
.

It is very well known fact that among all rectangles with the given perimeter the maximum area has a square 
whose side is one forth of the given perimeter.


In this problem, one forth of the perimeter is   = 6 cm.


Therefore, the maximum possible area is  6*6 = 36 cm^2.


Any area below or equal this value is achievable.


Any area above this value is not achievable.



So, the area 40 cm^2 (case A) is not achievable.   It is your ANSWER.


Any area below or equal to 36 cm^ is achievable.

Solved.

---------------

See the lesson
- A rectangle with a given perimeter which has the maximal area is a square
in this site.

RELATED QUESTIONS
the perimeter of a rectangle is 24cm. if the length is triple the width, find the area of (answered by macston)

The perimeter of a rectangle is 24cm. Express the area of the rectangle in terms of the... (answered by ewatrrr)

The length of a rectangle is three times its width, the perimeter of the rectangle is... (answered by josmiceli)

A rectangle 9cm long is equal in area to a square which has a perimeter of 24cm. Find the (answered by Cromlix)

1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm. Find... (answered by ikleyn,MathTherapy)

The length of a rectangle is twice its width. If the perimeter is 24cm, what is its... (answered by macston,addingup)

A rectangle has an area of 12 cm2. Its sides are of integer lengths in centimetres.... (answered by josgarithmetic)

well the perimeter of the original rectangle is 24cm, so how would the perimeter be... (answered by josgarithmetic)