Question

The coordinates of the vertices of a triangle are D(5,6), E(7,5), and F(4,3). Find the perimeter of the triangle.

Answer 1

We have to find the length of each side. We can use the distance formula as follows:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

For side DE:

`\begin{gathered} DE\text{ =}\sqrt[]{(7-5)^2+(5-6)^2} \\ DE\text{ =}\sqrt[]{4+1} \\ DE\text{ =}\sqrt[]{5} \end{gathered}`

For side EF:

`\begin{gathered} EF=\sqrt[]{(4-7)^2+(3-5)^2} \\ EF=\sqrt[]{9+4} \\ EF=\sqrt[]{13} \end{gathered}`

For side DF:

`\begin{gathered} DF=\sqrt[]{(4-5)^2+(3-6)^2} \\ DF=\sqrt[]{1+9} \\ DF=\sqrt[]{10} \end{gathered}`

Finally, the perimeter of the triangle DEF is = √5 + √13 + √10 ≈ 9