In a right-angled triangle XYZ, with a right angle at Y, W is the mid-point of side YZ. XY = 8√3 cm and XZ = 16 cm. Find the length of XW.
Show answer & explanation
Correct answer: C
Explanation
Given:
∠Y = 90°
XY = 8√3
XZ = 16
W is the midpoint of YZ
By the formula:
Pythagoras Theorem Median Formula
m² = (2a² + 2b² − c²) / 4
YZ² = XZ² − XY²
= 16² − (8√3)²
= 256 − 192 = 64
YZ = 8
a = XY = 8√3
b = XZ = 16
c = YZ = 8
XW² = (2(8√3)² + 2(16)² − 8²) / 4
= (2 × 192 + 2 × 256 − 64) / 4
= (384 + 512 − 64) / 4
= 832 / 4 = 208
XW = √208 = 4√13 cm