Question

tw is a midsegment of δuvx. if uv = p - 49 and tw = p - 54, what is the value of p? (with a triangle diagram labeled x, t, u, w, v)

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of a midsegment of a triangle is half the length of the parallel side. So, \(UV = 2\times TW\).

Step2: Substitute the given expressions

Substitute \(UV=p - 49\) and \(TW=p - 54\) into the equation \(UV = 2\times TW\). We get \(p-49=2(p - 54)\).

Step3: Expand the right - hand side

Using the distributive property \(a(b - c)=ab-ac\), where \(a = 2\), \(b=p\), and \(c = 54\), we have \(p-49=2p-108\).

Step4: Solve for \(p\)

Subtract \(p\) from both sides: \((p - 49)-p=(2p-108)-p\), which simplifies to \(-49=p - 108\). Then add 108 to both sides: \(-49 + 108=p-108 + 108\).

Answer:

\(p = 59\)