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:

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

Step-by-step 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 = $\frac{h}{2}$  (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).