Mathematics
Grade6
Easy

Question

Find the perimeter of the rectangle whose coordinates are A (-33, 20), B (-33, 28), C (-4, 28), D (-4, 20)

  1. 70    
  2. 75    
  3. 74    
  4. 232    

Hint:

We are given 4 coordinates of corner of a rectangle ABCD. We are asked to find the perimeter of the rectangle. Perimeter means the length of the border of the shape. To solve this question, we will find any two adjacent sides. Once we find the adjacent sides, we will use the formula for perimeter of a rectangle.

The correct answer is: 74


    The given rectangle is ABCD
    The points are:
    A = (-33,20)
    B = (-33,28)
    C = (-4,28)
    D = (-4,20)
    We have to find the length of the adjacent sides of rectangle ABCD
    To find the length we will use the following criteria:
    1) If x coordinate is same, we will find the absolute distance using y coordinate. An absolute distance is the length of the point from the respective axis. If x coordinate is same then its length is measured from x axis. It is a positive quantity.
    2) If y coordinate is same we will use the x coordinate to find absolute distance.
    3) If the points are in same quadrant, we will have to subtract the absolute distances to find length.
    4) If the points are in adjacent quadrants, we will have to add the absolute distances to find length.
    We will consider the side AB as length and BD as breadth.
    A and B have same signs so they are in same quadrant. And B and C have different signs so they are in adjacent quadrants.
    We will find the length of side AB.
    For the points A and B, x coordinate is same. We will find the absolute distance using y coordinate. It is distance from x axis.
    Absolute distance of the point A = |20|
    Absolute distance of the point B = |28|
    Length of AB = |28| – |20|
    = 28 - 20
    = 8
    Length of the rectangle is 8 units.
    We will find the length of side BC
    For the points B and C, y coordinate is same. We will find the absolute distance using x coordinate. It is distance from y axis.
    Absolute distance of the point B = |-33|
    Absolute distance of the point C = |-4|
    Length of BC = |-33| - |-4|
    = 33 - 4
    = 29
    Breadth of the rectangle is 29 units.
    The formula for perimeter is 2(length + breadth)
    Perimeter of rectangle ABCD = 2(length + breadth)
    = 2(8 + 29)
    = 2(37)
    = 74 units.
    Therefore, perimeter of the rectangle is 74 units.



    For such questions, we have to see if the points of the rectangle are in same quadrant or adjacent quadrants. We can use distance formula to find the length of sides of rectangle too.

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