Question

triangle RST is an equilateral triangle; . line TX is perpendicular of line RS.

If RT = 8 , then TX= ?

a. 3 sqrt(3)
b. 4 sqrt(3)
c. sqrt(5)
d. 3 sqrt(2)

Answer 1

Equilateral Triangle means all sides are equal, and all angles are equal (60).

TX bisects the triangle, therefore it bisects one of the angles. You now have two triangles with angles of 30-60-90.

RT is the hypotenuse of one of those triangles, and since RT=RS=ST, (1/2)RS = the length base of the triangle.

\[A^{2}+B^{2}=C^{2}\]
\[\Large (TX)^{2}+4^{2}=8^{2}\]

Solve for TX.