Question

A circle with the longest chord of 8 has the same areea as an equilateral triangle with side x. What is the height of that triangle.

Explanations please - thanks :)

Answer 1

i know the diam is 8
a = 16*3.14 = 50.24

Answer 2

so area of triangle is equal ot 50.24, right?

Answer 3

Longest chord is the diameter, so r=4
Area of circle = area of triangle
\[\pi r ^{2}=\frac{\sqrt{3}}{4}(abc)^{\frac{2}{3}}\]
\[\pi r ^{2}=\frac{\sqrt{3}}{4}(x ^{3})^{\frac{2}{3}}\]
\[\pi r ^{2}=\frac{\sqrt{3}}{4}(x ^{2})\]
x=10.77
h could be 9.31