We are given that Ruby created a pattern to sew flowers onto a quilt by drawing a regularpentagon and semicircles onto each side. Let's draw a diagram of this pattern.
Notice that the side of the regular pentagon is a diameter of a semicircle. This means that the radius of each semicircle is 3.52=1.75 inches.
Now let's recall that that the circumference of a semicircle is the half of the circumference of a circle. By using this information we can find the arc length of one semicircle.
1/2*2π * 1.75 = 1.75π
Next, to find the circumference of the whole flower we will multiply the arc length of one semicircle by 5.
5* 1.75π=8.75π
Finally, since we want to find how many inches of gold trim Ruby needs to edge 10 flowers, we will multiply the circumference of one flower by 10.
10*8.75π=87.5π≈ 275
Ruby needs approximately 275 inches to edge 10 flowers.
