Question

What radius of a circle is required to inscribe an equilateral triangle with an area of 35.074 in2 and an altitude of 7.794 in? (round to nearest tenth)

Answer 1

check the picture below.

Answer 2

`r`≈
`5.2 in`

Explanation:

It is given that a circle is required to inscribe an equilateral triangle with an area of
`35.074 in^2` and an altitude of
`7.794 in`,

Also, we know that the centroid divides the altitude into 2:1 form, thus

`r=(2)/(3)(h)`

Substituting the value of an altitude, we have

`r=(2)/(3)(7.794)`

`r=5.196 in`

`r`≈
`5.2 in`

Therefore, the radius of the circle is
`5.2 inches`.