Triangle $abc$ has vertices at $a(5,8)$, $b(3,-2)$, and $c(6,1)$. the point $d$ with coordinates $(m, n)$ is chosen inside the triangle so that the three small triangles $abd$, $acd$ and $bcd$ all have equal areas. what is the value of $10m + n$?

10m + n = 49

Explanation:

Point D will be the centroid of ABC. To find the centroid we use formula.

Given the coordinates of the three vertices of a triangle ABC,

the centroid D coordinates are given by -

m = (x₁ + x₂ + x₃)/3      &      n = (y₁ + y₂ + y₃)/3

m =

m =

and

n =

n =

Now we will find the value of 10m+n

=

=

= 49

So, 10m + n = 49

That's the final answer.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

180 square centimeters

step-by-step explanation: