Question

ΔHAT is similar to ΔCAN.

Answer 1

Answer:

The value of y is $\frac{10}{3}$. It can be written as $3\frac{1}{3}$.

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

$\frac{CN}{HT}=\frac{AC}{AH}$

$\frac{CN}{HT}=\frac{AC}{AC+CH}$

$\frac{y}{6}=\frac{5}{5+4}$

$\frac{y}{6}=\frac{5}{9}$

$y\times 9=5\times 6$

$y\times 9=30$

Divide both sides by 9.

$y=\frac{30}{9}$

$y=\frac{10}{3}$

$y=3\frac{1}{3}$

Therefore the value of y is $\frac{10}{3}$. It can be written as $3\frac{1}{3}$.

Answer 2

In similar triangles, the ratios of corresponding sides are equal.

This means

y/6=5/(4+5)

Cross multiply

y=5*6/(4+5)=30/9=10/3 (or 3 1/3)