Question

if $uv = p$ and $wy = p - 24$, what is the value of $p$?
triangle diagram with markings indicating midsegments or congruent segments
$p = \square$

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side. Here, \(WY\) is the mid - segment and \(UV\) is the third side. So, \(WY=\frac{1}{2}UV\).

Step2: Substitute the given expressions

Given \(UV = p\) and \(WY=p - 24\), substitute into the equation \(WY=\frac{1}{2}UV\). We get \(p-24=\frac{1}{2}p\).

Step3: Solve the equation for \(p\)

Multiply both sides of the equation \(p - 24=\frac{1}{2}p\) by \(2\) to get \(2(p - 24)=p\).
Expand the left - hand side: \(2p-48 = p\).
Subtract \(p\) from both sides: \(2p-p-48=p - p\).
So, \(p=48\).

Answer:

\(48\)