Answer:
The distance of QR is 54 units
Step-by-step explanation:
In the isosceles triangle, The height drawn from the vertex angle to the base bisects the base
In ΔPQR
∵ PQ = PR
∴ Δ PQR is an isosceles triangle
∵ P is the vertex angle
∵ QR is the base
∵ PS ⊥ QR
→ By using the fact above
∴ PS bisects QR
∴ S is the midpoint of QR
→ That means S divided QR into 2 equal parts QS and SR
∵ QS = SR
∵ QS = 6n + 3
∵ SR = 4n + 11
→ Equate them to find n
∴ 6n + 3 = 4n + 11
→ Subtract 4 n from both sides
∵ 6n - 4n + 3 = 4n - 4n + 11
∴ 2n + 3 = 11
→ Subtract 3 from both sides
∵ 2n + 3 - 3 = 11 - 3
∴ 2n = 8
→ Divide both sides by 2
∴ n = 4
→ Find the length of QS by substitute x in its expression by 4
∵ QS = 6(4) + 3 = 24 + 3
∴ QS = 27
∵ QS = SR
∴ SR = 27
∵ QR = QS + SR
∴ QR = 27 + 27
∴ QR = 54 units
∴ The distance of QR is 54 units
