Answer:
AX = 20
AY = 15
Explanation:
The perimeter is ...
P = AC +CB +BA = (AX +XC) +CB +(BY +YA)
128 = AX +32 + 37 +24 +AY
35 = AX +AY
The ratios of corresponding sides are proportional:
AX/AY = XC/YB = 32/24 = 4/3
This tells us ...
AX = 4/3·AY
Substituting, we get ...
35 = (4/3)AY +AY = (7/3)AY
(3/7)·35 = 15 = AY
AX = 35 -AY = 20
The side measures are AX = 20, AY = 15.