Question
A rectangular garden has a length of 100 cm. The ratio
of the width of the garden to the side of a square flower bed is 5: 8. If the ratio of the perimeter of the garden to the perimeter of the flower bed is 5:12, what is the area of the garden?Solution
Let the width of the garden be 5x cm. Let the side of the square flower bed be 8x cm. Perimeter of the garden = 2 * (length + width) = 2 * (100 + 5x) Perimeter of the flower bed = 4 * side = 4 * 8x = 32x 5: 12 = (2 * (100 + 5x)): (32x) Simplifying, we get: 5 * 32x = 12 * 2 * (100 + 5x) 160x = 2400 + 120x 40x = 2400 x = 60 Width of the garden = 5x = 5 * 60 = 300 cm Area of the garden = length * width = 100 * 300 = 30,000 cm² Ans. B
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