Question 488212: The perimeter of this block of land is 72 m. Find:
a the length of the block
b the area of the block.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you don't have enough information to determine the length of the block or the area of the block.
the area of the block will differ depending on the length of the block and the width of the block.
the length of the block requires you to know the width of the block before determining what it is.
here's some examples:
72 is the perimeter.
you are given that.
the perimeter is determined by the equation 2L + 2W = perimeter.
you have 2L + 2W = 72
if you let W = 8, then 2W = 16 and the formula becomes:
2L + 16 = 72
subtract 16 from both sides of this equation to get:
2L = 56
divide this equation by 2 to get:
L = 28
your dimensions are:
L = 28
W = 8
the area is L * W which equals 28 * 8 which equals 224 square meters.
now, assume W = 16.
this means that 2W = 32.
this means that 2L + 2W = 72 becomes 2L + 32 = 72
subtract 32 from both sides of that equation to get:
2L = 40
divide both sides of that equation to get
L = 20
your dimensions are:
L = 20
W = 16
the area is now L * W = 20 * 16 = 320 square units.
Given that the perimeter is 72 meters, the length is dependent on the width and the area is dependent on the length times the width.
without knowing the width, you can have many possible lengths depending on the dimension of the width that you choose.
here's a table that shows you the possible lengths and widths with a perimeter of 72.
these are all integers in multiples of 4.
if you assume real numbers that could include fractional parts of a whole number, then the list can be endless.
Perimeter
Length Width Area
72 4 68 272
72 8 64 512
72 12 60 720
72 16 56 896
72 20 52 1040
72 24 48 1152
72 28 44 1232
72 32 40 1280
72 36 36 1296
72 40 32 1280
72 44 28 1232
72 48 24 1152
72 52 20 1040
72 56 16 896
72 60 12 720
72 64 8 512
72 68 4 272
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