Question

Given the ABC DEF find the value of x and y

Answer 1

Answer: x = 7.2, y = 7.5

Step-by-step explanation:

Similar triangles have the same proportions.

Since ABC ≅  DEF, then $\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}$

Let's solve for x:

   $\dfrac{BC}{EF}=\dfrac{AC}{DF}$

⇒ $\dfrac{5}{4}=\dfrac{9}{x}$

⇒ $5(x)=4(9)$

⇒ $x = \dfrac{4(9)}{5}$

⇒ $x = \dfrac{36}{5}$

⇒ $x = 7.2$

Let's solve for y:

   $\dfrac{BC}{EF}=\dfrac{AB}{DE}$

⇒ $\dfrac{5}{4}=\dfrac{y}{6}$

⇒ $5(6)=4(y)$

⇒ $\dfrac{5(6)}{4}=y$

⇒ $\dfrac{30}{4}=y$

⇒ $7.5=y$

Answer 2

Answer:

y = 7.5 units

x = 7.2 units          

Step-by-step explanation:

We are given the following information:

ΔABC $\sim$ 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:

$\displaystyle\frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF}$

Putting values:

$\displaystyle\frac{y}{6} = \frac{9}{x} = \frac{5}{4}\\\\y = 6\times \frac{5}{4} = 7.5\text{ units}\\\\x = 9\times \frac{4}{5}=7.2\text{ units}$