What is the value of x?
A triangle is shown with variable expressions on the sides and a segment drawn inside the triangle between the left and right sides.
The inner segment is marked parallel to the lower segment of the triangle.
The left segment between the parallel segments is labeled x plus 5.
The left segment above the inside segment to the upper vertex is labeled x.
The right segment above the inside segment to the upper vertex is labeled x minus 2.
The right segment between the parallel segment is labeled x plus 1.
(1 point)
Responses
5
5
2.5
2.5
7.5
7.5
10
7.5
To find the value of x, we can use the property that when a line is parallel to one side of a triangle, it creates similar triangles with proportional side lengths.
In this case, we can set up a proportion with the segments x+5 and x+1:
(x+5)/(x+1) = x/(x-2)
Cross multiply to get:
x(x+1) = (x+5)(x-2)
x^2 + x = x^2 + 3x - 10
x = 7.5
Therefore, the value of x is 7.5.