Question

in the diagram below of triangle nop, q is the midpoint of $overline{np}$ and r is the midpoint of $overline{op}$. if $qr = 48 - 5x$, and $no=-16 + 6x$, what is the measure of $overline{qr}$? answer attempt 1 out of 2 $qr=$

Explanation:

Step1: Use the mid - segment theorem

In \(\triangle NOP\), since \(Q\) is the mid - point of \(\overline{NP}\) and \(R\) is the mid - point of \(\overline{OP}\), by the mid - segment theorem, \(QR=\frac{1}{2}NO\).

Step2: Set up the equation

Given \(QR = 48-5x\) and \(NO=-16 + 6x\). Substitute into \(QR=\frac{1}{2}NO\), we get \(48-5x=\frac{1}{2}(-16 + 6x)\).

Step3: Solve the equation

Multiply both sides of the equation \(48-5x=\frac{1}{2}(-16 + 6x)\) by \(2\) to get \(96-10x=-16 + 6x\).
Add \(10x\) to both sides: \(96=-16 + 16x\).
Add \(16\) to both sides: \(112 = 16x\).
Divide both sides by \(16\): \(x = 7\).

Step4: Find the value of \(QR\)

Substitute \(x = 7\) into \(QR=48-5x\). Then \(QR=48-5\times7=48 - 35=13\).

Answer:

\( QR = 28 \)