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Question
The perimeter of a square garden is 48 m. A small flower bed covers 18 sq m area inside this garden. What is the area of the garden that is not covered by the flower bed? What fractional part of the garden is covered by flower bed? Find the ratio of the area covered by the flower bed and the remaining area.
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Solution
Let side of square garden be x cm.
Given that, perimeter of a square garden = 48 m
⇒ 4 × Side of a square = 48
⇒ 4x = 48
⇒ x = `48/4` = 12 m
Now, area of the square garden = (x)2 = (12)2 = 144 m2
Also, given, area of small flower bed cover inside the garden = 18 m2
∴ Area of the garden not covered by flower bed
= Area of square garden – Area of flower bed
= 144 – 18
= 126 m2
The fractional part of the garden covered by flower bed
= `"Area covered by flower bed"/"Total area of garden"`
= `18/144`
= `1/8`
Ratio of the area covered by the flower bed and remaining area
= `"Area covered by the flower"/"Area of remaining garden"`
= `18/126`
= `1/7`
Hence, the ratio of area covered by the flower bed and the remaining area is 1 : 7.
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