Answer:
Perimeter of triangle = 12 + 9 + 15
= 36 units
Therefore, option A is correct.
Step-by-step explanation:
The given points
From the table, it is clear the side containing the line segment joining the points (-4, 5) and (8, 5) is a straight horizontal line.
Thus, the length of the horizontal distance from the points (-4, 5) and (8, 5) will be:
8-(-4) = 12 units
From the table, it is clear the side containing the line segment joining the points (8, 5) and (8, -4) is a straight vertical line.
Thus, the length of the vertical distance from the points (8, -4) and (8, 5) will be:
5-(-4) = 9
Now, finding the length of the side containing the segment (8, -4) and (-4, 5) using the formula:
[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(-4-8\right)^2+\left(5-\left(-4\right)\right)^2}[/tex]
[tex]=\sqrt{\left(-4-8\right)^2+\left(5+4\right)^2}[/tex]
[tex]=\sqrt{12^2+9^2}[/tex]
[tex]=\sqrt{144+81}[/tex]
[tex]=\sqrt{225}[/tex]
[tex]=\sqrt{15^2}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a[/tex]
[tex]=15[/tex]
We know that the Perimeter of a rectangle is the length of all the sides of the triangle. Therefore, combining all the lengths of the line segments
Thus,
Perimeter of triangle = 12 + 9 + 15
= 36 units
Therefore, option A is correct.
