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allochka39001 [22]
3 years ago
14

What is the perimeter of ΔABC?

Mathematics
1 answer:
Serggg [28]3 years ago
6 0

Answer:

Choice D:  Perimeter = 5 + \sqrt{65} +  \sqrt{34}  units

Step-by-step explanation:

point B(9, 2)  , point C(4, 5),  point A (1,1)

Perimeter = D( A, C)  + D (A, B)  + D (B, C)

where D (A, C) =  distance between A and C

so...

D(A, C) = root ( (4 - 1)^2 + (5 - 1)^2) = 5   from a 3-4-5 right triangle.

D(A, B) = root( (9- 1)^2 + (2 -1)^2) = root( 64 + 1) = root(65)

D(B, C) = root( (9 -4)^2 + (2 -5)^2) = root (25 + 9) = root(34)

Perimeter = 5 + root(65) + root(34)

Perimeter = 5 + \sqrt{65} +  \sqrt{34}  units

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