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KIM [24]
3 years ago
5

The vertices of a triangle are located at P(0, 0), Q(8, 6), and R(-3, 4). What is the perimeter of this triangle?

Mathematics
1 answer:
alexgriva [62]3 years ago
4 0
I graphed the vertices and got a triangle but its very hard to solve its perimeter. Therefore, I identified right triangles to help me solve for the perimeter making each side the hypotenuse of each right triangle.
Pythagorean Theorem: a² + b² = c²
a = short leg ; b = long leg ; c = hypotenuse 

P(0,0) ; R(-3,4)
a = 3 ; b = 4 ; 
3² + 4² = c²
9 + 16 = c²
25 = c²
√25 = √c²
5 = c

P(0,0) ; Q(8,6)
a = 6 ; b = 8 
6² + 8² = c²
36 + 64 = c²
100 = c²
√100 = √c²
10 = c

Q(8,6) ; R(-3,4)
a = 2 ; b = 11
2² + 11² = c²
4 + 121 = c²
125 = c²
√125 = √c²
11.18 = c

Perimeter = 5 + 10 + 11.18 = 26.18
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Explanations:

  1. By definition, the quartiles split the data into four equal parts. The first quartile (Q1) will have 25% of the data below it.
  2. The second quartile is the exact same value as the median. This is because the median splits the data into two equal halves, i.e. is at the midpoint.
  3. There's not enough info. We can determine that 25% of the company makes more than $60,000, but we don't know how many people total work at the company. This info is missing.
  4. Subtract the third and first quartiles (Q3 and Q1) to get the interquartile range (IQR). So IQR = Q3 - Q1 = 45-21 = 24
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