Question
The area of a rectangle with length and breadth in the
ratio of 8:5, respectively, is 320 cm². If the perimeter of the rectangle is the same as the perimeter of a square, then find the length of each side of the square.Solution
ATQ, et the length and breadth of the rectangle be '8x' cm and '5x' cm, respectively. ATQ: '8x' X '5x' = 320 Or, 40x² = 320 Or, x² = 320 ÷ 40 = 8 Or, 'x' = ± √8 As length and breadth cannot be negative, therefore, 'x' = √8 Perimeter of a rectangle = 2 X (Length + Breadth) = 2 X (8x + 5x) = 2 X 13x = 2 X 13 X √8 = 26√8 cm Perimeter of a square = 4 X side Length of each side of the square = (26√8/4) = 6.5√8 cm
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