Question

use the figure on the right to find the value of x.
x = \square (type an integer or a decimal.)

Explanation:

Step1: Identify the theorem

In a triangle, if a perpendicular is drawn from the vertex to the hypotenuse and the triangle is isosceles (as indicated by the marks on the sides), the segments created on the hypotenuse are equal. So, \(2x = 4x - 8\).

Step2: Solve for x

Subtract \(2x\) from both sides:
\(0 = 2x - 8\)

Add 8 to both sides:
\(2x = 8\)

Divide by 2:
\(x = \frac{8}{2} = 4\)

Answer:

\(4\)