Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
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If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
Volume is the amount of space that a substance or object occupies, or that is enclosed within a container. It is measured in <span>Volumetric units. </span>
Answer:
Step-by-step explanation:
Three times a number x : 3x
Three times a number x increase by 4: 3x +4
Five times the number x: 5x
5x = 3x +4
Subtract 3x from both the sides.
5x - 3x = 3x +4 - 3x
2x = 4
Divide both sides by 2
2x/2 = 4/2
x=2
The number is 2
