Question

use the figure at the right. if jk = 6x + 20 and no = 25, what is the value of x? x = □

Explanation:

Step1: Use the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side. Here, \(JK = 2\times NO\).

Step2: Substitute the given expressions

Given \(JK = 6x + 20\) and \(NO=25\). Substitute into the equation \(6x + 20=2\times25\).

Step3: Solve the equation for \(x\)

First, simplify the right - hand side: \(2\times25 = 50\). Then the equation becomes \(6x+20 = 50\). Subtract 20 from both sides: \(6x=50 - 20\), so \(6x=30\). Divide both sides by 6: \(x=\frac{30}{6}\).

Answer:

\(x = 5\)