Question

the length of a rectangle is twice as long as the side of a square. the side of a square is 4 cm longer than the width of the same rectangle . if their areas are equal , find their dimensions .





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Answer 1

The dimensions of the square and rectangle can be calculated as follows:

• Let us consider-

1. Length of square as "a"
2. Length of rectangle as "l"
3. Width of rectangle as "b"

• We know that area of square = a² and area of reactngle =  l * b        

• Now, As per the question,

        l = 2a                       (eq 1)

       a = b+4                    (eq 2)

       a² = l * b                   (eq 3)

• Substituting the values of eq1 and eq2 in eq3, we get,

        a² = 2a (a-4)

        a² = 2a² - 8a

        a² = 8a

        a = 8

• Thus, l = 2a

                  l  = 16

         and,  b = a-4

                   b   = 4

• Therefore, a = 8, l = 16, and b = 4