Respuesta :

Answer:

y = 7.5 units

x = 7.2 units          

Step-by-step explanation:

We are given the following information:

ΔABC [tex]\sim[/tex] ΔDEF

We have to find the value of x and y.

When two triangles are similar, then the corresponding sides are in same proportion.

This can be written as:

[tex]\displaystyle\frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF}[/tex]

Putting values:

[tex]\displaystyle\frac{y}{6} = \frac{9}{x} = \frac{5}{4}\\\\y = 6\times \frac{5}{4} = 7.5\text{ units}\\\\x = 9\times \frac{4}{5}=7.2\text{ units}[/tex]

The measure of the length of the triangle side x is 7.2 and y is 7.5 units.

What are similar triangles?

If the two triangles are similar, the ratio of their sides and angles are in proportion.

  • The measure of the length AB is y, DE is 6.

  • The measure of the length AC is 9, DF is x.

  • The measure of the length BC is 5, EF is 4.

Therefore,

The triangles are in the same ratio;

[tex]\rm \dfrac{AB}{DE}=\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\[/tex]

[tex]\rm \dfrac{y}{6}=\dfrac{9}{x}=\dfrac{5}{4}\\\\\dfrac{9}{x}=\dfrac{5}{4}\\\\ 9\times 4= 5\times x\\\\36=5x\\\\x=\dfrac{36}{5}\\\\x=7.2 \ units\\\\\dfrac{y}{6}=\dfrac{5}{4}\\\\4\times y= 6 \times 5\\\\ 4y=30\\\\y = \dfrac{30}{4}\\\\y=7.5\ units[/tex]

Hence, the measure of the length of the triangle side x is 7.2 and y is 7.5 units.

To know more about Triangle click the link given below.

https://brainly.com/question/25813512

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