In ΔXYZ, ∠Y = 90 degrees and YN is perpendicular to XZ. If XY = 30 cm and XZ = 34 cm, then what is the value of YN?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. (240/17) cm.
Given ΔXYZ with ∠Y = 90° and YN perpendicular to XZ:
Use Pythagoras theorem to find YZ:
XY2 + YZ2 = XZ2
302 + YZ2 = 342
900 + YZ2 = 1156
YZ2 = 256
YZ = 16 cm
Now, use the area formula to find YN:
Area = (1/2) × XY × YZ = (1/2) × 30 × 16 = 240 cm2
Area = (1/2) × XZ × YN = (1/2) × 34 × YN
240 = 17 × YN
YN = 240 / 17