Question

vz || wy. find wx.
v w x
15
14
y
35
z
wx =
submit
work it ou

Explanation:

Step1: Identify Similar Triangles

Since \( \overline{VZ} \parallel \overline{WY} \), by the Basic Proportionality Theorem (Thales' theorem), triangles \( \triangle XWY \) and \( \triangle XVZ \) are similar. So, the ratios of corresponding sides are equal: \( \frac{WX}{VX} = \frac{WY}{VZ} \). Let \( WX = x \), then \( VX = VW + WX = 15 + x \). The length of \( WY = 14 \) and \( VZ = 14 + 35 = 49 \).

Step2: Set Up Proportion

Substitute into the proportion: \( \frac{x}{15 + x} = \frac{14}{49} \). Simplify \( \frac{14}{49} = \frac{2}{7} \), so \( \frac{x}{15 + x} = \frac{2}{7} \).

Step3: Solve for \( x \)

Cross - multiply: \( 7x = 2(15 + x) \). Expand the right - hand side: \( 7x = 30 + 2x \). Subtract \( 2x \) from both sides: \( 7x - 2x = 30 \), which gives \( 5x = 30 \). Divide both sides by 5: \( x=\frac{30}{5}=6 \).

Answer:

\( 6 \)