Question

use the figure at the right. if $jk = 7x + 21$ and $no = 21$, what is the value of $x$?

Explanation:

Step1: Apply 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 \(\triangle LJK\), so \(NO=\frac{1}{2}JK\).

Step2: Substitute the given values into the equation

Given \(NO = 21\) and \(JK=7x + 21\). Substituting into \(NO=\frac{1}{2}JK\), we get \(21=\frac{1}{2}(7x + 21)\).

Step3: Solve the equation for \(x\)

Multiply both sides of the equation \(21=\frac{1}{2}(7x + 21)\) by \(2\) to get \(42=7x + 21\).
Subtract \(21\) from both sides: \(42-21=7x\), so \(21 = 7x\).
Divide both sides by \(7\): \(x=\frac{21}{7}=3\).

Answer:

\(3\)