Question

$YZ\parallel WS$ and Y and Z are midpoints of WX and SX respectively. Also,
WY = 7 cm
XS = 18 cm
YZ = 10 cm
Find the length of side WX.

• A. WX = 7 cm
• B. WX = 14 cm
• C. WX = 20 cm
• D. WX = 15 cm

Answer 1

The correct option is B WX = 14 cm

Given: $YZ\parallel WS$ and Y and Z are mid-points of WX and SX.
Therefore, XS and XW are transversal to the parallel lines YZ and XS.
$\angle XZY=\angle XSW$ $\left(Correspondingangles\right)$
$\angle XYZ=\angle XWS$ $\left(Correspondingangles\right)$
$\angle YXZ=\angle WXS$ $\left(CommonAngle\right)$
Therefore, $\Delta XYZ\sim \Delta XWS$ $\left(ThroughAAAAxiomofSimilarity\right)$
Hence, the triangles will have equal ratio of their corresponding sides.
$\frac{WX}{YX}$ = $\frac{SX}{ZX}$ = $\frac{WS}{YZ}$
$\frac{WX}{7}$ = $\frac{18}{ZX}$ = $\frac{WS}{10}$ $SinceWY=YX$
Applying Mid-point theorem, we get
WS = 2 YZ
WS = 2 (10)
= 20 cm
Substituting the value in $\frac{WX}{7}$ = $\frac{WS}{10}$ , we get
$\frac{WX}{7}$ = $\frac{20}{10}$
$\frac{WX}{7}$ = $2$
$WX$ = $14cm$