Question

use the figure at the right. if ( jk = 5x + 8 ) and ( no = 24 ), what is the value of ( 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 parallel to the third side and half its length. Here, \(NO\) is a mid - segment of \(\triangle LJK\) (since \(N\) is the midpoint of \(JL\) and \(O\) is the midpoint of \(LK\)), so \(NO=\frac{1}{2}JK\).

Step2: Substitute the given values into the equation

Given \(NO = 24\) and \(JK=5x + 8\). Substituting into \(NO=\frac{1}{2}JK\), we get \(24=\frac{1}{2}(5x + 8)\).
Multiply both sides of the equation by \(2\) to get rid of the fraction: \(2\times24=5x + 8\), which simplifies to \(48=5x + 8\).

Step3: Solve for \(x\)

Subtract \(8\) from both sides: \(48−8 = 5x\), so \(40 = 5x\).
Divide both sides by \(5\): \(x=\frac{40}{5}\).

Answer:

\(x = 8\)