Question

if sw = 2x + 44 and tv = x + 64, what is tv?
tv = \boxed{}

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, \( SW = 2TV \) (since \( TV \) is the mid - segment and \( SW \) is the third side). Given \( SW=2z + 44 \) and \( TV=-z + 64 \). Substitute into the equation \( 2z + 44=2(-z + 64) \).

Step2: Solve the equation for \( z \)

Expand the right - hand side: \( 2z + 44=-2z+128 \). Add \( 2z \) to both sides: \( 2z+2z + 44=-2z + 2z+128 \), which gives \( 4z+44 = 128 \). Subtract 44 from both sides: \( 4z+44 - 44=128 - 44 \), so \( 4z=84 \). Divide both sides by 4: \( z=\frac{84}{4}=21 \).

Step3: Find the value of \( TV \)

Substitute \( z = 21 \) into the formula for \( TV \). \( TV=-z + 64 \). Replace \( z \) with 21: \( TV=-(21)+64 \). Calculate \( TV=43 \).

Answer:

\( 43 \)