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ICSE Class 10 Answered

The length of a rectangular garden is twice the length of a square garden and its breadth is 2 m less than that of the square. The area of the rectangular garden is 21  metre square more than that of the square. Find the dimensions of the rectangle.  
Asked by khushdab | 01 Apr, 2020, 04:43: PM
answered-by-expert Expert Answer
Let l and b be the length and breadth of the rectangle.
Let 'a' be the side of the square.
According to the question, l = 2a, b = a - 2
Area of rectangle = Area of square + 21
lb = a2 + 21
Substituting the values of l and b in the above equation, we have
(2a)(a - 2) = a2 + 21
a2 - 4a -21 = 0
(a - 7)(a + 3) = 0
a = 7 or a = -3
Since the length of side of the square can't be negative, therefore a = 7.
Therefore, l = 2a = 14 and b = a - 2 = 5
Hence, the dimension of the rectangle ais 14m x 5m.
Answered by Renu Varma | 01 Apr, 2020, 06:26: PM

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