Use the Side-Splitter Theorem to solve for x (Round to the nearest tenth) (1 point) Responses 5.6 5.6 6 6 5 5 5.5
To use the Side-Splitter Theorem, we need the side lengths of two similar triangles that are formed by a transversal intersecting two parallel lines.
Let's call the sides of the smaller triangle as a, b, and x, and the corresponding sides of the larger triangle as A, B, and X. According to the Side-Splitter Theorem, we have the following ratio:
a/A = b/B = x/X
In this case, we are given the side lengths of the larger triangle (A = 6, B = 5.5) and the side lengths of the smaller triangle (a = 5, b = 5.6). We need to solve for x.
We can set up the proportion:
5/6 = 5.6/5.5 = x/X
Cross-multiplying, we get:
5 * 5.5 = 6 * 5.6 = x
27.5 = 33.6 = x
Therefore, x ≈ 27.5 (rounded to the nearest tenth).