Question

A rhombus has the same perimeter as the circumference of a circle. If the side of the rhombus is 2.2 m, find the radius of the circle.

Answer 1

We have:

The side of a rhombus = 2.2 m
Let C be the circumference of a circle having a radius r cm. Then,

the perimeter of the rhombus = 4$\times \mathrm{side}$ = 4 x 2.2 = 8.8 m.
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We know:

Perimeter of the rhombus = Circumference of the circle

$$\begin{gathered} \Rightarrow 8.8\mathrm{m}=2\mathrm{\pi r} \\ \Rightarrow r=\left(\frac{8.8}{2\mathrm{\pi }}\right)\mathrm{m}=\left(\frac{8.8\times 7}{2\times 22}\right)\mathrm{m}=\left(\frac{88\times 7}{2\times 22\times 10}\right)\mathrm{m} \\ \Rightarrow r=\left(\frac{2\times 7}{10}\right)\mathrm{m}=1.4\mathrm{m}. \end{gathered}$$
The radius of the circle is 1.4 m.