Question

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

Answer 1

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.