if the area of rectangle is 24 square centimetres and its length is 6 CM then its perimeter
Answers
Step-by-step explanation:
What is the area of a rectangle whose perimeter is 24 cm?
The problem with this question is that it does not provide enough information to give a definitive answer. You have two variables, the length (L) and width (W) of the rectangle. But based on the information given, you can only write one equation: 2L + 2W = 24. You can simplify this equation to L + W = 12. But then you are stuck.
There is a logical domain (set of acceptable answers) for L and W. Each must be a real number greater than zero and less than 12. However, within that domain, there are still an infinite number of possible values for L and W.
Normally with this type of problem, another fact is given regarding length and width. With two variables, you need two different equations to solve simultaneously in order to come up with a definite answer.
Given the limited information, all you can do is solve for one variable in terms of the other (W = 12 - L) then write area as a formula in terms of one variable within the domain of the variable.
Area = L * (12-L) = 12L - L^2, where 0<L<12.
In a calculus class, you might develop this formula in order to determine what values of L and W would make a rectangle of maximum area. So it can be useful to know how to express the area of a rectangle in terms of one of its sides.
Could be many different areas.
The rectangle could be 2 cm x 10 cm, area would be 20 sq cm
The rectangle could be 4 cm x 8 cm, area would be 32 sq cm
The rectangle could be 5 cm x 7 cm, area would be 35 sq cm
The rectangle could be 6 cm x 6 cm (a square IS a rectangle), area = 36 sq cm
The rectangle could be 3 cm x 9 cm, area is 27 sq cm
The rectangle could be 1 cm by 11 cm, area is 11 sq cm
They all have a perimeter of 24 cm.
2(l+b)=24
l+b=12
In this problem no sufficient data is given. So we assume the area such that
the sum of the length and breadth=12
If l=11,b=1 Area=11 sq cm
l=10,b=2 area=20
l=9 b=3 area=27
l=8 b=4 area=32
l=7 b=5 area=35
If l=6 and b=6 it becomes a square
In rectangle length>breadth
So all other pairs are not possible
Answer:
Area of rectangle is 24sqcm
Length = 6cm
Breadth= ( consider as B)
length×breadth= Area of the rectangle
6×b= 24
6b= 24
w= 24/6=4cm
Perimeter of the rectangle:
2×(l+b)
2×(6+4)
12+8= 20cm