Answer:
The expression that can be used to find the length of the side of the triangle represented by the vertices (5, 5), and (7, -3) is given as follows;
A. [tex]\sqrt{\left (5-7 \right )^{2}+\left (5-(-3) \right )^{2}}[/tex]
Step-by-step explanation:
The formula for finding the length, 'l', of a line given the (x, y) coordinates is presented as follows;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
The given coordinates of the vertices of the triangular garden are;
(-2, 3), (5, 5), and (7, -3)
Therefore, the length of the side of the triangle that is represented by the vertices (5, 5) and (7, -3) is found by substituting the 'x', and 'y', values as follows;
[tex]l_{(Side \, of \, the \, triangle)} = \sqrt{\left (5-7 \right )^{2}+\left (5-(-3) \right )^{2}}[/tex]
Which can be further simplified as follows;
[tex]\sqrt{\left (5-7 \right )^{2}+\left (5-(-3) \right )^{2}} = \sqrt{\left (-2 \right )^{2}+\left (8 \right )^{2}} = \sqrt{68} = 2 \cdot \sqrt{17}[/tex]