If Triangle R$U is an equilateral triangle. RT bisects US. r and y is: x=4√3; y=9.
Equilateral triangle
UT=ST=4 (bisector)
UT+ST = US
US=4+4
US=8
Equilateral triangle RS=8
Using Pythagorean theorem to determine x
RT²+ST²=RS²
x²+4²=8²
x²=64-16
x²=48
x=√48
x=√16×3
x=4√3
Hence:
Find y using the fact that RT bisect ST:
m∠RTS=90° perpendicular
m∠TRS=(2y+12)°
m∠RST=2×m∠TRS
m∠RST=2(2y+12)°
m∠RST=(4y+24)°
Hence:
m∠RTS+m∠RST+m∠TRS=180°
Substitute
90°+2y+12+4y+24=180°
Collect like terms
6y+126=180
Subtract 126
6y=54°
Divide both side by 6
y=54°/6
y=9
Angles equilateral triangle= 60°, hence
2y+12 = 60/2 bisector
2y+12=30
collect like term
2y=30-12
2y=18
Divide both side by 2
y=18/2
y=9
Therefore r and y is: x=4√3; y=9.
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