find length of segment

Question

Triangle XYZ below is an isosceles triangle with legs XY and ZY. QR and QS are perpendicular bisectors of triangle XYZ. Find the length of segment QR if
QR = ½ x and QS = -½ x + 4.

Answer 1

Hello Julia,

Do QR and QS bisect the legs of the triangle XYZ?

If so then they would be congruent, given that this is an isosceles triangles and those two sides are the same length.

Therefore 1/2x = -1/2x +4. If you add 1/2x to both sides you get x = 4.