Question

the graph shows the endpoints of one side of an equilateral triangle. determine the perimeter of the triangle. enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the triangle: units

Explanation:

Step1: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 1,y_1=-1,x_2 = 7,y_2 = 10$.
$d=\sqrt{(7 - 1)^2+(10+ 1)^2}=\sqrt{6^2+11^2}=\sqrt{36 + 121}=\sqrt{157}\approx 12.53$

Step2: Calculate perimeter of equilateral triangle

Since it's an equilateral triangle, all sides are equal. Perimeter $P$ of an equilateral triangle with side length $s$ is $P = 3s$. Here $s=\sqrt{157}$, so $P = 3\sqrt{157}\approx3\times12.53 = 37.59$

Answer:

$3\sqrt{157}\approx37.59$