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Question
A wire, when bent in the form of a square encloses an area of 484 cm2. Find :
(i) one side of the square ;
(ii) length of the wire ;
(iii) the largest area enclosed; if the same wire is bent to form a circle.
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Solution
(i)
Area of Square = 484 cm2
Side of Square = `sqrt("Area")` = `sqrt484` = 22 cm
(ii)
Perimeter, i.e. length of wire = 4 x 22 = 88 cm
(iii)
Circumference of circle = 88 cm
2πr = 88
`2 xx 22/7 xx r = 88`
`r = (88 xx 7)/(2 xx 22)`
r = 14 cm
∴ The largest area enclosed = `pir^2`
= `22/7 xx 14 xx 14`
= 616 cm2
Hence (i) 22 cm (ii) 88 cm (iii) 616 cm2
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