For this case we have that both triangles are similar, then the following relationship is fulfilled:
[tex]\frac {A_ {1}} {l_ {1}} = \frac {A_ {2}} {l_ {2}}[/tex]
Where:
[tex]A_ {1} \ and \ {l_ {1}[/tex]correspond to the area and side of the largest triangle
Substituting:
[tex]\frac {382} {42} = \frac {A_ {2}} {30}\\A_ {2} = \frac {30 * 382} {42}\\A_ {2} = 272.8571429\\A_ {2} = 273 \ ft ^ 2[/tex]
Thus, the area of the smallest triangle is [tex]273 \ ft ^ 2[/tex]
Answer:
[tex]273 \ ft ^ 2[/tex]
