Answer:
x = 7; y = 4
Step-by-step explanation:
∆ABC is an isosceles triangle.
∴ AC = BC and
(1) 3x - 5 = y + 12
∆ACD is an equilateral triangle.
∴ AC = AD and
(2) 3x - 5 = 5y - 4
From (1) and (2),
y + 12 = 5y - 4
y + 16 = 5y
4y = 16
(3) y = 4
Substitute (3) into (1)
3x - 5 = 4 + 12
3x - 5 = 16
3x = 21
x = 7
x = 7; y = 4
Check:
AC = 3x - 5 = 3(7) - 5 = 21 - 5 = 16
BC = y + 12 = 4 + 12 = 16
AD = 5y - 4 = 5(4) - 4 = 20 - 4 = 16
OK
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