Question

△ XYZ∼ △ DEF, YZ is 10 meters, ​ XZ ​ is 15 meters, and EF is 8 meters. What is ​ DF?

Answer 1

Im not for sure on this but i would say DF is 13

Answer 2

△ XYZ∼ △ DEF, YZ is 10 meters, ​ XZ ​ is 15 meters, and EF is 8 meters. What is ​ DF?

Solution:

As, △ XYZ∼ △ DEF , so the ratio of sides of triangle is equal.

So, we have, $\frac{XY}{DE} =\frac{YZ}{EF} =\frac{XZ}{DF}$

Using, $\frac{YZ}{EF} =\frac{XZ}{DF}$

So, we get,$\frac{10}{8} =\frac{15}{DF}$

Now, to solve for DF, we must simplify

Simplifying,$\frac{10}{8} =\frac{5*2}{4*2}=\frac{15}{DF)$

$\frac{5}{4} =\frac{15}{DF}$

To simplify, Let us multiply by 4*DF on both sides

$\frac{5*4DF}{4} =\frac{15*4DF}{DF}$

$\frac{5DF}{1} =\frac{15*4}{1}$

So, 5 DF=15*4=60

To solve for DF, let us divide by 5 on both sides

$\frac{5}{5} DF=\frac{60}{5}$

$\frac{1}{1} DF=\frac{12}{1}$

So, DF=12meters