Question

3. A wire in the shape of a rectangle of dimensions 14.2 cm x 10 cm is opened up to form a square and a circle turn by turn. Find the side of the square and radius of the circle.
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Answer 1

so the circumference of both square and circle made by the wire would be same

so the perimeter of rectangle

2(l+b) = p 2(l+b)=p

2×(14.2+10) = p 2×(14.2+10)=p

48.4 cm 48.4cm

【i】 so of both square and circle the value would be same

$48.4 = \: 4× side$

$side = \frac{48.4}{4} \: cm$

side = 14.1 cm side=14.1cm

so the side of square would be 14.1 cm

【ii】 now the circumference of the circle would be same as perimeter of rectangle

$48.4 = 2 × \frac{22}{7} × r$

$r = \frac{48.4×7}{22×2}$

$r = \frac{338.8}{44}$

r = 7.7

so the radius is 7.7 cm