Question

In the following shape, two semicircles

have been placed at the end of a
rectangle whose length is twice its height.
Which of the following gives the length
around this figure in terms of the
semicircle's radius, r?

Answer 1

The length around the figure in terms of r is 2r (
`\pi` + 4).

Explanation:

The perimeter of an object is the total length of the boundary of the object.

The figure consists two similar semicircle and a rectangle.

Adding the two semicircles, a complete circle is formed. The circumference of a circle = 2
`\pi`r.

The rectangle has a length which is twice its height.

i.e l = 2h

But,

r =
`(h)/(2)` (the diameters of the semicircles equal the height of the rectangle)

⇒ h = 2r

Thus, one side length of rectangle = 2 × 2r (l = 2 × h)

= 4r

The length around the figure in terms of r is:

= 2
`\pi`r + 4r + 4r

= 2
`\pi`r + 8r

= 2r (
`\pi` + 4)

The length around the figure in terms of r is 2r (
`\pi` + 4).