Question

su is a midsegment of \\( \triangle tvw \\).
if \\( vw = z + 57 \\) and \\( su = 2z \\), what is the value of \\( z \\)?

Explanation:

Step1: Use the midsegment theorem

The midsegment theorem states that the length of a midsegment of a triangle is half the length of the third side. So, \( SU=\frac{1}{2}VW \).

Step2: Substitute the given expressions

Given \( VW = z + 57 \) and \( SU = 2z \), substitute into the equation \( 2z=\frac{1}{2}(z + 57) \).
Multiply both sides by 2 to get \( 4z=z + 57 \).

Step3: Solve for \( z \)

Subtract \( z \) from both sides: \( 4z−z=57 \), so \( 3z = 57 \).
Divide both sides by 3: \( z=\frac{57}{3}=19 \).

Answer:

\( 19 \)