Question 67

In the figure, ABCD is a rectangle and each circle has diameter 4 cm. The length BC is equal to

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Solution

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Since, $$\triangle{PQR}$$ and $$\triangle{QRS}$$ are similar equilateral triangles. 

Side of $$\triangle{PQR}$$ = Diameter of any circle = 4 cm

$$Area of \triangle{PQR} = \frac{\sqrt{3}}{4}PR^{2} = \frac{1}{2} * QR * \frac{PS}{2}$$

$$\frac{\sqrt{3}}{4}4^{2} = \frac{1}{2} * 4 * \frac{PS}{2}$$

$$PS = 4\sqrt{3}$$

Lenght of BC = PS + 2 + 2 = $$4\sqrt{3} + 4 = (4{\sqrt{3} + 1}) cm$$

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