Answer:
The value of y is [tex]\frac{10}{3}[/tex]. It can be written as [tex]3\frac{1}{3}[/tex].
Step-by-step explanation:
It is given that ΔHAT is similar to ΔCAN. The corresponding sides of similar triangle are proportional.
Since ΔHAT is similar to ΔCAN, therefore
[tex]\frac{CN}{HT}=\frac{AC}{AH}[/tex]
[tex]\frac{CN}{HT}=\frac{AC}{AC+CH}[/tex]
[tex]\frac{y}{6}=\frac{5}{5+4}[/tex]
[tex]\frac{y}{6}=\frac{5}{9}[/tex]
[tex]y\times 9=5\times 6[/tex]
[tex]y\times 9=30[/tex]
Divide both sides by 9.
[tex]y=\frac{30}{9}[/tex]
[tex]y=\frac{10}{3}[/tex]
[tex]y=3\frac{1}{3}[/tex]
Therefore the value of y is [tex]\frac{10}{3}[/tex]. It can be written as [tex]3\frac{1}{3}[/tex].
