Triangle ABC has coordinates A(−6,2), B(−3,6), and C(5,0). Find the perimeter of the triangle. Round your answer to the hundredths place (2 decimal places) I will give brainliest
Answers
Answer:
26.18 units
Step-by-step explanation:
You could use distance formula three times to calculate the length of each side. Add the three lengths to find the perimeter. However, (see image) if you look at a graph of these points, two of the sides are the hypotenuse of a right triangle that have known, integer values--Pythagorean triples. The sides are 3-4-5 and the other is 6-8-10. We use the Pythagorean theorem to find the third side. See image.
11.18 + 5 + 10
= 26.18 units
The perimeter of triangle is 26.18.
What is triangle?A triangle is 2-dimensional closed curve. which has 3 sides, 3 angles and 3 vertices.
According to the question,
Triangle ABC has coordinates A(-6,2), B(-3,6), C(5,0).
Distance formula: √(x₂-x₁)² + (y₂-y₁)².
Points A and B are (-6,2) and (-3,6)
= √(-3-(-6))² + (6-2)²
= √9+16
= √25
=5.
Thus, point A and B has distance, S₁ = 5.
Points B and C are (-3,6) and (5,0)
Distance formula: √(x₂-x₁)² + (y₂-y₁)²
= √(5-(-3))² + (0-6)²
= √(8)² + (-6)²
= √(64+36)
=√100
=10.
Thus, point B and C has distance, S₂ = 10.
Points C and A are (5,0) and (-6,2)
Distance formula: √(x₂-x₁)² + (y₂-y₁)²
= √(-6-(5))² + (2-0)²
= √((-11)² + (2)²)
=√(121+4)
=√125
=5√5
Thus, point C and A has distance, S₃= 5√5.
Perimeter of triangle = S₁ + S₂+S₃
= 5 + 10 + 5√5
=15+5√5
=15+5(2.23606)
=15+11.1803
=26.1803 ≈ 26.18
Hence, the perimeter of triangle is 26.18.
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