Question

1. error analysis describe and correct the error in finding the perimeter of triangle b. the triangles are similar.

Explanation:

Step1: Find perimeter of Triangle A

$\text{Perimeter}_A = 10 + 6 + 12 = 28$

Step2: Identify ratio error

The proportion uses $\frac{5}{10}$ (small/large) but sets it equal to $\frac{\text{large perimeter}}{x}$. Correct ratio: $\frac{\text{Perimeter}_B}{\text{Perimeter}_A} = \frac{\text{Side}_B}{\text{Side}_A}$, so $\frac{x}{28} = \frac{5}{10}$.

Step3: Solve for $x$

$10x = 28 \times 5$
$10x = 140$
$x = \frac{140}{10} = 14$

Answer:

The error is that the ratio was set up incorrectly: the side length ratio (small triangle to large triangle) was paired with the large triangle's perimeter over the small triangle's perimeter instead of the small perimeter over the large perimeter. The correct perimeter of Triangle B is 14.