MathematicsEach side of a square field measures 21 m. Adjacent to this field, there is a rectangular field having its sides in the ratio 4:3. If the perimeters of both the fields are equal, the length of the rectangular field is ____ m.

Each side of a square field measures 21 m. Adjacent to this field, there is a rectangular field having its sides in the ratio 4:3. If the perimeters of both the fields are equal, the length of the rectangular field is ____ m.


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    Solution:

    Each side of a square field measures 21m. Adjacent to this field, there is a rectangular field having its sides in the ratio 4:3. If the perimeters of both the fields are equal, the length of the rectangular field is 24 m.
    Given the side of a square field is 21 m.
    Perimeter of square is,
    =4×side   = 4×21   = 84 m
    Length of the rectangular field = 4x.
    Breadth of rectangular field = 3x.
    Perimeter of rectangle is,
    =2× Length+breadth   = 2(4x + 3x)
    = 2(7x)
    = 14x
    Since, the perimeter of square and rectangle are the same.
    So, 84 = 14x.
    x= 84 14   x = 6
    The length is,
    =6×4 =24m  
    The length of the rectangular field is 24 m.
     
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