Step-by-step explanation:
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Answer:
x = 8.69
Step-by-step explanation:
we know that the perimeter of the dodecagon is 54, so each edge will be 54/12
54/12 = 4.5 cm
if we draw the lines to remove 6 vertices and form a hexagon, 6 triangles with 2 sides of 4.5 cm are formed.
we know that the angle of each vertex is 150 ° because it is a dodecagon
if we apply the law of cosines we can take the other side of the triangle, since we only need 2 side and the opposite angle to the side we want to know
a would be our x
b = 4.5
c = 4.5
A = 150°
a^2 = b^2 + c^2 - 2bc * cos (A)
x^2 = 4.5^2 + 4.5^2 - 2 * 4.5 * 4.5 * cos (150)
x^2 = 20.25 + 20.25 - 40.50 * -0.866
x^2 = 40.50 + 35.07
x = √ 75.57
x = 8.69
<span>A.three sides measuring 9 meters, 5 meters, and 5 meters
--> only one isosceles triangle
B.three sides measuring 6 inches, 3 inches and 9 inches
--> none triangle may be formed because 9 = 3 + 6 and there is a rule (the triangle inequality theorem) that states the length of any side must be less than the sum of the lengths of other two sides.
C.three angles measuring 25°, 25°, and 130°
--> 25 + 25 + 130 = 180 => you can construct many triangles with these angles
D.three angles measuring 55°, 25°, and 125°
--> 55 + 25 + 125 = 205 > 180 => you cannot construct any triangle with theses measures.
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Opposite number is like 8 and -8. And absolute value is like -8 and 8 or 9 and 9. The absolute value is always positive.
