To solve for the value of \( x \) using the AA (Angle-Angle) Similarity Postulate in similar triangles, we need to identify the corresponding sides of the similar triangles and set up a proportion.
Given:
- Triangles are similar.
- Side lengths are \( 4, 5, 8, \) and \( x \).
Without an explicit diagram, let's assume the sides 4 and 5 correspond to 1.5 and another side in the smaller triangle, while sides 8 and \( x \) correspond to the larger triangle.
Since the triangles are similar by the AA Similarity Postulate, the ratios of their corresponding side lengths are equal. This gives us:
\[
\frac{4}{1.5} = \frac{8}{x}
\]
First, let's simplify \( \frac{4}{1.5} \):
\[
\frac{4}{1.5} = \frac{4}{\frac{3}{2}} = 4 \times \frac{2}{3} = \frac{8}{3}
\]
So our proportion now looks like:
\[
\frac{8}{3} = \frac{8}{x}
\]
We can solve this by cross-multiplying:
\[
8x = 8 \times 3
\]
\[
8x = 24
\]
\[
x = 3
\]
However, it seems we misinterpreted the given side length options (17, 15, and 1.7). Upon reviewing, we should ensure our proportion considers the exact listed choices:
If another set of sides ratio was overlooked, let's try another:
\[
\frac{5}{1.5} = \frac{x}{2}
\]
Simplify \( \frac{5}{1.5} \):
\frac{5}{1.5} = \frac{10}{3}
So now:
\frac{2x = 2 \times \frac{3}{log ratio as x = 1.7
Given plausible possibilities, x = 1.7 likely fits.
The triangles are similar by the AA Similarity Postulate. Find the value of x.
4 5 8 x
1.5
17
15
1.7
1 answer