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

Answer:

Perimeter of the figure is 2r($\pi$ + 6)

Step-by-step explanation:

Perimeter of a shape is total length of the boundaries of the shape. In the given question, we have two semicircles and a rectangle.

The circumference of a circle = 2$\pi$r, thus the length of the arc of a semicircle = $\pi$r.

The height of the rectangle is h, radius 'r' of the semicircle = $\frac{h}{2}$

⇒                             h = 2r

The perimeter of a rectangle = 2(l +b).

Given that: the length is twice its height, so that:

length = 2h

Perimeter of the rectangle = 2 (2h + h)

                                            = 6h

But,        h = 2r

Perimeter of the rectangle = 6 × 2r  

                                            = 12r      

Perimeter of the figure in terms of the semicircle's radius = $\pi$r + 12r  + $\pi$r

                                                                                               = 2$\pi$r + 12r

                                                                                   = 2r($\pi$ + 6)