Answer:
[tex]A = 15[/tex] [tex]B = 20[/tex] [tex]C = 25[/tex]
[tex]D = 30[/tex] [tex]E = 40[/tex] [tex]F = 50[/tex]
[tex]D = 3[/tex] [tex]E = 4[/tex] [tex]F = 5[/tex]
Step-by-step explanation:
Given
Similar Triangles: ABC and DEF
[tex]A = 15[/tex]
[tex]B = 20[/tex]
[tex]C = 25[/tex]
Required
Determine the sides of DEF
No options were given, so I will solve on a general terms.
Since both triangles are similar, then the following relationship exists.
DEF = ABC * n
i.e.
[tex]D = A * n[/tex] [tex]E = B * n[/tex] [tex]F = C * n[/tex]
Where
[tex]n = Scale\ Factor[/tex]
Assume n = 2.
So, we have:
[tex]D = A * n[/tex]
[tex]D =15 *2[/tex]
[tex]D = 30[/tex]
[tex]E = B * n[/tex]
[tex]E = 20 * 2[/tex]
[tex]E = 40[/tex]
[tex]F = C * n[/tex]
[tex]F = 25 * 2[/tex]
[tex]F = 50[/tex]
Assume [tex]n = \frac{1}{5}.[/tex]
So, we have:
[tex]D = A * n[/tex]
[tex]D =15 *\frac{1}{5}[/tex]
[tex]D = 3[/tex]
[tex]E = B * n[/tex]
[tex]E = 20 * \frac{1}{5}[/tex]
[tex]E = 4[/tex]
[tex]F = C * n[/tex]
[tex]F = 25 * \frac{1}{5}[/tex]
[tex]F = 5[/tex]
So, the possible sides are:
[tex]A = 15[/tex] [tex]B = 20[/tex] [tex]C = 25[/tex]
[tex]D = 30[/tex] [tex]E = 40[/tex] [tex]F = 50[/tex]
[tex]D = 3[/tex] [tex]E = 4[/tex] [tex]F = 5[/tex]
