Answer:
x = 13, y = 26
The length of the sides of Δ QRS are QR = 104, QS = 468, RS = 76
Explanation:
In ΔRQS
∵ M is the mid-point of side RQ
→ That means M divide RQ into 2 equal parts RM and MQ
∴ RM = MQ
∵ RM = 4x
∵ MQ = 52
→ Equate them
∴ 4x = 52
→ Divide both sides by 4 to get x
∴ x = 13
∵ P is the mid-point of side QS
→ That means P divide QS into 2 equal parts QP and PS
∴ QP = PS
∵ QP = 9y
∵ PS = 234
→ Equate them
∴ 9y = 234
→ Divide both sides by 9 to get y
∴ y = 26
→ Find the length of each side
∵ RQ = 52 + 52
∴ RQ = 104
∵ QS = 234 + 234
∴ QS = 468
∵ RS = 38 + 38
∴ RS = 76
∴ The length of the sides of Δ QRS are QR = 104, QS = 468, RS = 76
Note: PS = 234 is wrong because it made the length of the sides QS = 468, which could not be because the sum of any 2 sides of a triangle must be greater than the 3rd side. So check it.