Question

Reasoning triangle $abc$ has a perimeter of $12$ units. the vertices of the triangle are $a(x,\ 2),\ b(2,-2)$ , and $c(-1,\ 2)$ . find the value of $x$ .

Answer 1

hmmm let's find the distance between B and C first off.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{-1}~,~\stackrel{y_2}{2})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ BC=√((~~-1 - 2~~)^2 + (~~2 - (-2)~~)^2) \implies BC=√((-1 -2)^2 + (2 +2)^2) \\\\\\ BC=√(( -3 )^2 + ( 4 )^2) \implies BC=√( 9 + 16 ) \implies BC=√( 25 )\implies BC=5`

hmmm if BC is that much, then AB + AC = 7, since AB + AC + BC = 12 which is the perimeter, Check the picture below.