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Question
The area of a square garden is equal to the area of a rectangular plot of length 160m and width 40m. Calculate the cost of fencing the square garden at Rs.12per m.
Solution
The area of a rectangle with length l and breadth b = A = l x b
∴ The area of the rectangular plot with length 160m and breadth 40m
= A
= 160 x 40
= area of the square garden
We know,
The area of a square with side s = s2
∴ s2 = 160 x 40
⇒ s = `sqrt(160 xx 40)`
= `sqrt(16 xx 4 xx 100)`
= 4 x 2 x 10
= 80m
The perimeter of a square with side
= P
= 4s
∴ The perimeter of a square with side 80
= 4 x 80
= 320m
The cost of fencing at the rate of Rs.12per m
= 320 x 12
= Rs.3840.
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