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Alenkinab [10]
3 years ago
6

13 The circumference of the circle and the perimeter of the rectangle are equal.

Mathematics
1 answer:
Zolol [24]3 years ago
8 0

Answer:

Step-by-step explanation:

Note:

Circumference of a circle = \pi d

Where d = diameter

We are given the diameter is 20cm, d = 20

Circumference of circle = \pi d = 20 \pi

Also, perimeter of a rectangle = 2 times length + 2 times width

We are told the length = 18 , width = x

Perimeter of rectangle = 2 times 18 + 2 times x

Perimeter of rectangle = 36 + 2x

The question also tells us that the circumference of the circle is EQUAL to the perimeter of the rectangle:

So this means:

Since Circumference of circle = 20\pi  ,

Perimeter of rectangle = 36 + 2x .

We can write:

Circumference of circle = perimeter of rectangle

20\pi   = 36 + 2x

Subtract 36 from both sides

20\pi - 36   = 2x

Divide both sides by 2 to solve for "x".

x = \frac{20\pi - 36 }{2}  = ?

Plug it into your calculator and then just round it to 1 decimal place.

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