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 cm², then what is the circumference (in m) of the circle ?

0.44 m

We know that,

Circumference of circle = 2πr

Given,

Height of triangle = 14 cm,

Area of Triangle = 56 cm²

Base of triangle is \(\frac{4}{7}\) times the diameter of the circle.

Let the base and height of the rectangle = b and h respectively

According to the question,

Area of triangle = 56cm²

\(\frac{(b × h) }{2}\) = 56

b × 14 = 112

b = 8 cm

Base of triangle = \(\frac{7}{4}\) $\times$ the diameter of the circle.

8 = \(\frac{4}{7}\) $\times$ the diameter

diameter = 14

Circumference of circle = 2πr

= 2 × \(\frac{22}{7}\)× 7

= 44cm = 0.44 m