Answer:
[tex]\large\boxed{y=3\sqrt5\approx6.7}[/tex]
Step-by-step explanation:
ΔABC and ΔDAC are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{DC}{AC}[/tex]
We have
[tex]AC=y\\BC=3+12=15\\DC=3[/tex]
Substitute:
[tex]\dfrac{y}{15}=\dfrac{3}{y}[/tex] cross multiply
[tex]y^2=(15)(3)\\\\y^2=45\to y=\sqrt{45}\\\\y=\sqrt{9\cdot5}\\\\y=\sqrt9\cdot\sqrt5\\\\y=3\sqrt5\\\\y\approx6.7[/tex]
