Mathematics
Grade6
Easy

Question

Find the perimeter of the rectangle whose coordinates are as follows

  1. 100    
  2. 120    
  3. 415    
  4. 400    

Hint:

We are given a rectangle plotted in x-y plane. 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: 100


    The given rectangle is ABCD
    The points are:
    A = (15,-10)
    B = (15,30)
    C = (25,30)
    D = (25,-10)
    We have to find the length of the adjacent sides.
    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 BC as breadth.
    From the given figure, we can see points A and B are in adjacent quadrants. And points B and C are in same 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 = |-10|
    Absolute distance of the point B = |30|
    Length of AB = |30| + |- 10|
    = 30 + 10
    = 40
    Length of the rectangle is 40 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 = |15|
    Absolute distance of the point C = |25|
    Length of BC = |25| - |15|
    = 25 - 15
    = 10
    Breadth of the rectangle is 10 units.
    The formula for perimeter of a rectangle is 2(length + breadth)
    Perimeter of the rectangle ABCD = 2(length + breadth)
    . = 2( 40 + 10)
    = 100 units
    Therefore, perimeter of the rectangle is 100 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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