60% of the circumference of a circle is cut to form a rectangle with it's length being 3 times it's width. The dimeter of the circle is 42cm.find the width of a rectangle.( use π = 22\7)what is the answer?

1
by jericrichard

2015-12-12T12:12:49+08:00

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First things we do is to find the Circumference of a circle using the formula
C = 2π(d/2) where, C is the circumference and d = diameter of the circle
we will use π=22/7 and d = 42 cm
C = 2(22/7)(42/2)
C = 2(22/7)(21)
C = (2)(22)(3)
C = 132

There are 60% of the circumference of a circle that is cut to form a rectangle.
We will get that 60% by multiplying it to the circumference to get the Perimeter of the rectangle.
P = (0.60)(132)
P = 79.2

Perimeter of the rectangle is
P = 2L + 2W, where P is the perimeter, L is the length, and W is the width

Since, length is 3 times its width, we will denote this as
L = 3W

So we have
P = 2L + 2W
79.2 = 2(3W) + 2W
79.2 = 6W + 2W
79.2 = 8W
79.2 / 8 = 8W / 8
9.9 = W
W = 9.9 cm

Therefore, the width of the rectangle is 9.9 cm.