The diameter of a circle is $$\frac{7}{4}$$ times of the base of a triangle, and the height of the triangle is 14 cm. If the area of the triangle is 56 $$cm^{2}$$, then what is the circumference (in m) of the circle?

The diameter of a circle is $$\frac{7}{4}$$ times of the base of a triangle.

$$\text{diameter of a circle}=\frac{7}{4}\times\ \text{base of a triangle}$$    Eq.(i)

height of the triangle is 14 cm. If the area of the triangle is 56 $$cm^{2}$$.

area of the triangle = $$\frac{1}{2}\times\ base\times height$$

$$56 = \frac{1}{2}\times\ base\times 14$$

$$4 = \frac{1}{2}\times\ base$$

base of a triangle = 8 cm Eq.(ii)

Put Eq.(ii) in Eq.(i).

= $$7\times\ 2$$

= 14 cm

Circumference of the circle = $$\pi\ \times\ diameter$$

= $$\frac{22}{7}\times\ 14$$

= $$22\times2$$

= 44 cm

= 0.44 m [As we know that 100cm = 1m. Then 1cm = 0.01m. So 44 cm = $$0.01\times44$$ = 0.44 m]