Answer:
QR = 20
Explanation:
You want the measure of side QR of isosceles triangle PQR with congruent sides PQ and QR marked 5x and 3x+8, respectively.
Congruent sides
The sides of the isosceles triangle are congruent, so we have ...
PQ = QR
5x = 3x +8
2x = 8 . . . . . . . subtract 3x
x = 4 . . . . . . . divide by 2
QR = 3x +8 = 3(4) +8 = 20 . . . . . . find the length of QR
The measure of QR is 20 units.
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Additional comment
You will recognize that the segment QS is both the altitude and median of the triangle. That means the triangle is isosceles, so symmetrical about QS.
If you need a formal proof, you can observe that QS is congruent to itself, so the two right triangles are congruent by LL (or SAS).