Two sides of an equilateral triangle have lengths x+2 and -2x+20 which could be the length of the third side: 14-x or 2x+4? a. 2x + 4 only b. both 14 - x and 2x + 4 c. 14 - x only d. neither 14 - x nor 2x + 4

An equilateral triangle has 3 equal sides by definition.

so we know that x+2 = -2x+20 because we're told that those are both lengths of the triangle's sides. let's solve for x.

x+2 = -2x + 20
add 2x to both sides.
3x + 2 = 20
subtract 2 from both sides.
3x = 18
divide both sides by 3.
x = 6

now, let's find the length of the sides. plug 6 into one side, which is x+2.
6+2 = 8. so each side's length must be equal to 8. let's just check to make sure we didn't make a mistake. if this is correct, then -2x + 20 should also = 8.

-2(6) + 20
-12 + 20
8.

so we know that the sides = 8. let's see if 14 - x or 2x+4 are equal to 8 when we plug in 6 for x.

14 - 6 = 8. so 14-x could be a length for a side.

2(6) + 4 = 12 + 4 = 16. so 2x + 4 can not be a length for a side.

the answer is 14 - x only, or C.