Exercise 2 Page 328

Examining the given diagram, we can see that ∠ PSQ and ∠ QSR are adjacent congruent angles. Therefore, SQ forms a bisector of ∠ PSR. Moreover, the segments connecting Q with the sides of ∠ PSR are both perpendicular to the sides. This means that their length is the distance from each side to Q.

According to the Angle Bisector Theorem, if a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle. In our case, since Q lies on SQ, we know that it is equidistant from the sides of ∠ PSR. Therefore, QP and QR have equal lengths. QP=QR This allows us to equate the given expressions for their lengths to solve for x.

We found that x=3, so let's substitute its value into the expression of QP. 6x ⇒ 6( 3) ⇒ 18 Therefore, QP=18.