Question
The area of a rectangular field is 24% of the area of a
square field with a perimeter of 80 meters. If the rectangular field has a perimeter of 40 meters, determine its length.Solution
ATQ, Length of each side of the square ield = 80/4 = 20 metres Area of square ield = 20 × 20 = 400 m2 Area of rectangular ield = 0.24 × 400 = 96 m2 Let length and breadth of the rectangular ield is ‘l’ metres and ‘b’ metres, respectively. So, 2(l + b) = 40 Or, l + b = 20 So, (l – b)2 = (l + b)2 – 4lb = 400 – 4 × 96 = 16 So, l – b = 4 So, length of the rectangle = (20 + 4)/2 = 12 metres
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