Answer:
[tex]r[/tex]≈[tex]5.2 in[/tex]
Step-by-step explanation:
It is given that a circle is required to inscribe an equilateral triangle with an area of [tex]35.074 in^2[/tex] and an altitude of [tex]7.794 in[/tex],
Also, we know that the centroid divides the altitude into 2:1 form, thus
[tex]r=\frac{2}{3}(h)[/tex]
Substituting the value of an altitude, we have
[tex]r=\frac{2}{3}(7.794)[/tex]
[tex]r=5.196 in[/tex]
[tex]r[/tex]≈[tex]5.2 in[/tex]
Therefore, the radius of the circle is [tex]5.2 inches[/tex].
