If AMNP is an equilateral triangle, find x and the measure of each side
So, if is equilateral triangle, then each side has the same length. First, denote each side with the following letters:
A = 4x - 25
B = x + 14
C = 6x - 51
So:
A = B = C
Then, for example, we can choose the equation A= B , that is:
4x - 25 = x + 14
moving all the terms to the left side of the equation we have:
4x - 25 - x - 14 = 0
then
(4x - x) - (25 + 14) = 0
then
3x - 39 = 0
so
3x = 39
leaving the x alone we have
x = 39 / 3 = 13
replacing this value in the sides A, B and C, we have:
Side A = 4x - 25 = 4(13) - 25 = 52 - 25 = 27
Side B = x + 14 = 13 + 14 = 27
Sice C = 6x - 51 = 6(13) - 51 = 78 - 51 = 27
That is the answer.