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To find the value of x, we can use similar triangles. Since the right triangle formed by the angle bisector is similar to the larger triangle, we can set up a proportion using the corresponding sides.
We know that the upper side of the larger triangle is x and the lower side is 11.2. The upper part of the right side above the angle bisector is 5.4 and the lower part is 6.3.
Setting up the proportion:
(5.4 / 6.3) = (x / 11.2)
Cross multiply:
6.3x = 60.48
Divide by 6.3 to solve for x:
x = 60.48 / 6.3 ≈ 9.6
Therefore, the value of x is approximately 9.6 to the nearest tenth.
Answer: x = 9.6