Question

if vw = p and ux = 2p - 93, what is the value of p?
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p = \square

Explanation:

Step1: Use the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the midpoints of two sides) is half the length of the third side. Here, \(UX\) is the mid - segment and \(VW\) is the third side. So, \(UX=\frac{1}{2}VW\).
Given \(VW = p\) and \(UX=2p - 93\), we substitute into the formula: \(2p-93=\frac{1}{2}p\).

Step2: Solve the equation for \(p\)

Multiply both sides of the equation \(2p - 93=\frac{1}{2}p\) by \(2\) to get rid of the fraction:
\(2(2p - 93)=p\).
Expand the left - hand side: \(4p-186 = p\).
Subtract \(p\) from both sides: \(4p - p-186=p - p\), which simplifies to \(3p-186 = 0\).
Add \(186\) to both sides: \(3p-186 + 186=186\), so \(3p=186\).
Divide both sides by \(3\): \(p=\frac{186}{3}\).

Answer:

\(p = 62\)