Question
Consider a rectangle where the length to breadth ratio
is 4:3. Given that the area of the rectangle is 48 cm², a square is constructed using the rectangle's diagonal as its side. Calculate the perimeter of this square.Solution
Let the length and the breadth of the rectangle be '4a' cm and '3a' cm ATQ, Area of the rectangle = length X breadth 48 = (4a X 3a) Or, a2 = (48/12) = 4 So, 'a' = ±2 But length can't be negative, so 'a' = 2. Length of diagonal of the rectangle = {(length) 2 + (breadth) 2 }1/2 Length of the diagonal of the rectangle = {(4a) 2 + (3a)2}1/2 = (25a2) 1/2 = 5a = 10 cm So, side of the square = length of diagonal of rectangle = 10 cm Therefore, perimeter of the square = (4 X 10) cm = 40 cm
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