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Scalene Triangle

Step-by-step explanation:

To classify the triangle we have to find the lengths of each side.

Side AB

d= √  (−1−(−3))2+(4−2)2√  

d= √  (2)2+(2)2

d= √  4+4

d=√  8

d=2.828427 approximately 2.8

Side BC

d= √  (3−(−1))2+(−4−4)2

d= √  (4)2+(−8)2

d= √  16+64

d=8–√0

d=8.944272 approximately 8.9

Side AC

d=  √  (3−(−3))2+(−4−2)2

d=  √  (6)2+(−6)2

d=  √  36+36

d=  √  7 2

d=8.485281 approximately 8.5

Since no sides are the same length, it is a scalene triangle.

I hope this helps!

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step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240