Question

the perimeter of a semicircle is 108 cm what is the perimeter of the square drawn on the diameter of the semicircle ​

Answer 1

Answer:

Step-by-step explanation:

the perimeter of the semi-circle would be the diameter plus the circumference of half of the circle.  

They want to know the perimeter of a square using the diameter of the sem-circle as ONE side, so the perimeter of the square would be 4 times the ONE side.

We should recall:

diameter = 2 times the radius     circumference of a cirlce = 2π r

How do we find the diameter of the of the semi circle?

The perimeter of the semi circle is given as 108 cm

Perimeter of the semicirle =    2r + π r         diameter plus semi circumference

                                  108   =   r ( 2 + π)           factor out the r and solve for r

                     108 / (2 + π)   =   r                       divide both sides by ( 2 + r)

Now we know r, the perimeter of the squqre is 4 times 2r  or  8r

           perimeter of square = 8  [ 108 / (2 + π) ]               π  I used 3.14

                                             =  864 / 5.14

                                             =   168.1 cm       I got rounded to nearest tenth    

When I re-checked by work I found a few math,  logic and calculation errors.  Please re-check my answer for any more mistakes.