Respuesta :
Answer:
Alberto is incorrect. Perimeter is 42 units.
Step-by-step explanation:
Given:
The vertices of the triangle are [tex]S(-6.5, -8.5), T(2.5, -8.5),U(2.5, 3.5), \textrm{ and } V(-6.5, 3.5).[/tex]
Perimeter of a triangle of length [tex]l[/tex] and width [tex]b[/tex] is given as:
[tex]P=2(l+b)[/tex]
Here, [tex]l=ST,b=TU[/tex]
Distance between two points [tex]A(x_{1},y_{1})[/tex] and [tex]B(x_{1},y_{2})[/tex] is given as:
[tex]AB=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
So, the length ST is,
[tex]l=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\l=\sqrt{(2.5-(-6.5))^{2}+(-8.5-(-8.5))^{2}}\\l=\sqrt{9^{2}+0}=9[/tex]
Width TU is,
[tex]b=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\b=\sqrt{(2.5-2.5))^{2}+(3.5-(-8.5))^{2}}\\b=\sqrt{0+12^{2}}=12[/tex]
Therefore, the perimeter is given as:
Perimeter = [tex]2(l+b)=2(9+12)=2(21)=42[/tex] units.
Hence, the perimeter written by Alberto is incorrect as perimeter is not 18 units bu 42 units.
