Mathematics
Grade6
Easy

Question

Find the perimeter of rectangle ABCD.

  1. 10    
  2. 14    
  3. 16    
  4. 8    

Hint:

We are given a rectangle ABCD plotted on a x-y plane. We are given the coordinates of the corners of the rectangle. Using this information, we are asked to find the perimeter of the rectangle ABCD. Perimeter is a total length of the boundary of the shape it’s enclosing. We can do this by finding the sides of the rectangle and adding them.

The correct answer is: 16


    The given coordinates of the corner are as follows
    A = (3,1)
    B = (-2,1)
    C = (-2,-2)
    D = (3, -2)
    Now, we have to find the length of each side.
    Length means we have to find the distance between each points. To find the distance between the points, we will use this distance formula.
    d space equals square root of left parenthesis x subscript 2 space minus space x subscript 1 right parenthesis squared space space space plus space left parenthesis space y subscript 2 space minus space y subscript 1 space end subscript right parenthesis squared end root   
      Let’s find the sides one by one
    Side AB has two points A and B. We will find the distance between them.
              .   
                            A B space equals space square root of left parenthesis negative 2 space – space 3 right parenthesis squared space plus space left parenthesis 1 space – space 1 right parenthesis squared end root
space space space space space space equals square root of left parenthesis negative 5 right parenthesis hat 2 space plus space 0 end root
space space space space space space equals space square root of 25
space space space space space space equals space 5 space u n i t s
    So, the distance of AB is 5 units
    Side BC has two points B and C. We will find the distance between them.

    B C space equals space square root of left square bracket 2 minus space left parenthesis negative space 2 right parenthesis right square bracket squared space plus space left parenthesis negative 2 space – space 1 space right parenthesis squared end root
space space space space space space space equals square root of left parenthesis negative 2 space plus space 2 right parenthesis squared space plus space left parenthesis space minus 3 right parenthesis to the power of 2 space end exponent end root
space space space space space space space equals square root of 0 plus space 9 end root
space space space space space space space equals 3 space u n i t s
    So, the distance of BC is 3 units.
    Side CD has two points C and D. We will find the distance between them

    C D space equals space square root of left square bracket 3 space minus space left parenthesis negative 2 right parenthesis right square bracket squared space plus space left square bracket negative 2 space minus space left parenthesis negative 2 right parenthesis right square bracket squared end root
space space space space space space space equals square root of left parenthesis 3 space plus space 2 space right parenthesis squared space plus space left parenthesis negative 2 space plus space 2 right parenthesis squared end root
space space space space space space space equals square root of 5 squared space plus space 0 space end root
space space space space space space space equals 5 space u n i t s space
    So, the distance CD is 5 units
    Side DA has two points D and A. We will find distance between them.

    D A space equals space square root of left parenthesis 3 space – space 3 right parenthesis squared space plus space left square bracket space 1 space – space left parenthesis negative 2 right parenthesis space right square bracket squared end root
space space space space space space equals square root of 0 space plus space left parenthesis 1 space plus 2 right parenthesis squared end root
space space space space space space equals square root of 3 squared end root
space space space space space space equals 3 space u n i t s
    So, the distance DA is 3 units.
    Now we have all fours sides. So, to find the perimeter, we just have to add the sides.
    Perimeter of ABCD = AB + BC + CD + DA
    = 5 + 3 + 5 + 3
    = 16 units
    Therefore, perimeter of given rectangle is 16 units.

    Instead of finding all four sides, we can just find any two adjacent sides. We can use the forumula of perimeter of rectangle 2(l + b). This distance formula is more useful when the sides of rectangle are not exactly parallel to the coordination axis. We can find length is simpler way as one of the component is zero. Say side AB is parallel to y axis, so it's y component is zero.

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