Answer:
Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.
Step-by-step explanation:
Given the vertices of a triangle as: A(3, 5), B(− 1, 5), and C(3,− 6)
Since A and B are on the same y-coordinate, we have that:
AB = 3-(-1)=4 Units
Since A and C are on the same x-coordinate, we have that:
AC=5-(-6)=11 Units
Next, we determine the distance BC using the distance formula.
Given: B(− 1, 5), and C(3,− 6)
[tex]BC=\sqrt{(3-(-1))^2+(-6-5)^2}\\= \sqrt{(4)^2+(-11)^2}=\sqrt{137}$ Units[/tex]
Therefore:
Perimeter of the Triangle
[tex]= 4+11+\sqrt{137}\\ =15+\sqrt{137}$ Units\\=26.7 Units[/tex]
On plotting the triangle, it forms a right triangle such that the:
Base = 4 Units
Height = 11 Units
Therefore:
Area of a triangle [tex]=\dfrac12 *Base*Height[/tex]
Therefore:
Area of the Triangle = 0.5 X 4 X 11
=22 Square Units.
Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.
