Question

Triangle XYZ is an isosceles triangle with legs XY and ZY. Segments QR and QS are perpendicular bisectors of triangle XYZ. Find the length of segment QS if QR = ½ x + 2 and QS = x - 10.

Answer 1

In this item, we are to determine the value of x first and substitute the computed value to determine the lengths of QR and QS. Since we are given that two segments are perpendicular bisector of the isosceles triangle then, their lengths should also be equal.
QR = QS
Substituting with the given equation for each.
x/2 + 2 = x - 10

Multiply both sides of the equation by 2,
x + 4 = 2x - 20
Transpose all terms with variables to one side of the equation and the constants to the other.
x - 2x = -20 - 4
-x = -24
x = 24

QR: x/2 + 2 = 24/2 + 2 = 14
QS: x - 10 = 24 - 10 = 14

ANSWER: QR = QS = 14