A triangle has sides of lenth 4, 7, and x.

Mathematics
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A triangle has sides of length 4,7,and x. Which of the following could be the value of x? Indicate ALL such values. 2.9 4.5 6.25 7 12
Apr 29th, 2015

For the lengths of a triangle sides a, b and c there necessary and sufficient
a<b+c, b<a+c, c<a+b (triangle inequality).

Here
x=12 is impossible because 12>4+7=11
x=7 is possible
x=6.25 possible
x=4.5 possible
x=2.9 impossible (7>4+2.9, must be <)

[actually, x>0, x<7+4=11 and x>7-4=3, x in (3; 11)]

So the answer is 4.5, 6.25, 7.

Apr 29th, 2015

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