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 ?
Answer & explanation
Correct answer: option 1
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