Question 551748: Is it possible for a triangle to have side lengths of 19 cm, 13 cm , and 7 cm? why?
Found 3 solutions by Alan3354, nyc_function, KMST:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Is it possible for a triangle to have side lengths of 19 cm, 13 cm , and 7 cm? why?
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Yes, it is.
Why not?
Here are the angles in degrees.
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cos(A) = -143/182 A = 141.7867893
cos(B) = 241/266 B = 25.0396596
cos(C) = 481/494 C = 13.17355111
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The other tutor pointed out that 19^2 <> the sum of 7^2 + 13^2. That means it's not a right triangle.
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The longest side, 19, has to be less than the sum of the other 2, which it is.
The shortest side, 7, has to be more than the difference of the other 2, which it is.
So it's valid for a triangle.
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If you can find the angles as I did, it's proof of validity.
Answer by nyc_function(2741)  (Show Source):
You can put this solution on YOUR website! It is not possible to have a right triangle with the given sides where 19 represents the hypotenuse.
The reason is that in this case the sum of the squares of sides 7 and 13 DOES NOT equal the hypotenuse 19 squared.
LOOK:
7^2 + 13^2 = 19^2
49 + 169 = 361
218 DOES NOT EQUAL 361.
Understand?
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! YES. Because 13+7>19.
If you connect two sticks of length 13 cm and 7 cm
(blue and red in the figure) at one end with a hinge, 
the free ends could be at a distance of up to 20 cm (13 cm + 7 cm).
You get the 20 cm distance when the ends of the sticks are aligned.
If the sticks are at any angle other than 180 degrees, the ends of the sticks would be 3 points not aligned and would form a triangle.
The distance between the free ends of the sticks, measured along a straight line (black), is shorter that the distance from one free end, going throung the hinge, to the other free end (blue+red).
In geometry, that means that the length of a side of a triangle is less than the sum of the lengths of the other two sides.
At a struck stop, it is stated as "a straight line is the shortest distance between two points."
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