Can the sides of a triangle have lengths 4, 14, and 15?

Answer 1

can a triangle have sides 4, 14, 15? Yes.

no side can be smaller than the difference of the other two sides. no side can be larger than the sum of the other two sides. c<a+b, c>a-b.

15<14+4

15<18

4>15-14

4>1

or you could try heron's formula for the area

if it's an imaginary area, it's not a triangle

p=(15+14+4)/2 = 23/2 = 11.5

Area = sqr[p(p-a)(p-b)(p-c)

Area = sqr[(11.5)(11.5-15)(11.5-14)(11.5-4)]

=sqr[11.5(-3.5)(-2.5)(7.5)] > 0 as the negative factors cancel

= about 27.5 >0

27.5 is not an imaginary area