What is the value of x to the nearest tenth? The figure is not drawn to scale. The lower side of the larger triangle equals 11.2. The upper side of the larger triangle equals x. The upper part of the right side above the angle bisector equals 5.4. The lower part of the right side below the angle bisector equals 6.3. (1 point) Responses x = 2.1 x = 2.1 x = 3.4 x = 3.4 x = 9.6 x = 9.6 x = 13.1
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