Question

Both triangles are similar. The area of the larger triangle is about 382 ft.². Which is the best approximation for the area of the smaller triangle?
Answer options: 325, 137, 195, 273

Answer 1

For this case we have that both triangles are similar, then the following relationship is fulfilled:

$\frac {A_ {1}} {l_ {1}} = \frac {A_ {2}} {l_ {2}}$

Where:

$A_ {1} \ and \ {l_ {1}$correspond to the area and side of the largest triangle

Substituting:

$\frac {382} {42} = \frac {A_ {2}} {30}\\A_ {2} = \frac {30 * 382} {42}\\A_ {2} = 272.8571429\\A_ {2} = 273 \ ft ^ 2$

Thus, the area of the smallest triangle is $273 \ ft ^ 2$

Answer:

$273 \ ft ^ 2$