Question

Given a rectangle with a fixed perimeter of 24 meters, if we increase the length by 1m the width and area will vary accordingly. Use the following table of values to look at how the width and area vary as the length varies.
What do you observe? Write your observations in your notebooks.

Length (in m)	1	2	3	4	5	6	7	8	9
Width (in m)	11	10	…….	…….	…….	…….	…….	…….	…….
Area(in $ {{\text{m}}^2} $ )	11	20	…….	…….	…….	…….	…….	…….	…….

Answer 1

Hint:From the question it is clear that the perimeter of the rectangle is 24 meters. The perimeter of the rectangle is given by, where l=length and w=width. Now, we can find the width value from the given length and perimeter value. Finally we can find the area by Area= Length*Width

Complete step-by-step answer:
Given, Perimeter of Rectangle= 24 meters
 $ \Rightarrow $ $ 2 \times \left( {{\text{l + w}}} \right) $ =24
 $ \Rightarrow $ $ {\text{l + w}} $ = $ \dfrac{{24}}{2} = 12 $ meters
 $ \Rightarrow $ w = 12 – l
Therefore, from the table we can now find the width values as length varies
That is, if l = 3 $ \Rightarrow $ w = 12 - 3 = 9
If l =4 $ \Rightarrow $ w = 12 – 4 =8
If l =5 $ \Rightarrow $ w = 12 – 5 =7
If l =6 $ \Rightarrow $ w = 12 – 6 =6
If l =7 $ \Rightarrow $ w = 12 – 7 =5
If l =8 $ \Rightarrow $ w = 12 – 8 =4
If l =9 $ \Rightarrow $ w = 12 – 9 =3
Now, we have both length and width values
Therefore, Area of rectangle = $ {\text{l}} \times {\text{w}} $
Where l = length and w = width
From the above values, if l = 3, w = 9 $ \Rightarrow $ Area = $ 3 \times 9 $ = $ 27{\text{ }}{{\text{m}}^2} $
 If l = 4, w = 8 $ \Rightarrow $ Area = $ 4 \times 8 $ = $ {\text{32 }}{{\text{m}}^2} $
If l = 5, w = 7 $ \Rightarrow $ Area = $ 5 \times 7 $ = $ {\text{35 }}{{\text{m}}^2} $
If l = 6, w = 6 $ \Rightarrow $ Area = $ 6 \times 6 $ = $ {\text{36 }}{{\text{m}}^2} $
If l = 7, w = 5 $ \Rightarrow $ Area = $ 7 \times 5 $ = $ {\text{35 }}{{\text{m}}^2} $
If l = 8, w = 4 $ \Rightarrow $ Area = $ 8 \times 4 $ = $ {\text{32 }}{{\text{m}}^2} $
If l = 9, w = 3 $ \Rightarrow $ Area = \[9 \times 3\]=\[{\text{27 }}{{\text{m}}^2}\]
From the above calculations:

Length (in m)	1	2	3	4	5	6	7	8	9
Width (in m)	11	10	9	8	7	6	5	4	3
Area (in $ {{\text{m}}^2} $ )	11	20	27	32	35	36	35	32	27

Note: If we don’t remember the formula for the perimeter of the rectangle we can add the sides of it, which is length + width + length + width. That is the sum of two times of length and two times of width. If the length and width are equal it forms a square then the perimeter will be four times of the side and the area will be square of the side.