Answer:
[tex]D E F = 196[/tex]
Step-by-step explanation:
Given
[tex]ABC = 56, 64\ and\ 72[/tex]
[tex]Largest\ of\ D E F = 252[/tex]
Required
Determine the smallest side of DEF
Since both sides are similar, then the sides of DEF can be calculated using:
[tex]D E F = k * ABC[/tex]
First, we need to solve for k
From the given parameters
[tex]D E F = 252[/tex] when [tex]ABC = 72[/tex]
This is so because these are the largest sides of both triangles respectively
[tex]D E F = k * ABC[/tex]
[tex]252 = k * 72[/tex]
Divide through by 72
[tex]252/72 = k * 72/72[/tex]
[tex]k=252/72[/tex]
[tex]k=3.5[/tex]
We make use of the same formula to determine the length of the smallest side.
The smallest of ABC is 56, so we have:
[tex]D E F = k * ABC[/tex]
[tex]D E F = 3.5 * 56[/tex]
[tex]D E F = 196[/tex]
Hence, the smallest side of DEF is 196
