The area of a rectangle and the square of its perimeter are in the ratio 1 ∶ 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio ?
Explanation:
Suppose l = length of the rectangle and b = breadth of the rectangle.
Therefore, the area of the rectangle = lb and the perimeter of the rectangle = 2(l + b)
Therefore,
lb[2(l+b)]2=125 i.e. ιb(l+b)2=425
Substituting the options, we can see that only option (c) i.e., 1 : 4 matches.
Hence, option (c).
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