In an acute angled triangle XYZ, XP is an altitude drawn on side YZ. O is a point on XP such that XY = 12 cm, OY = 5 cm, and OZ = 9 cm, then find the length of XZ.
Show answer & explanation
Correct answer: C
Explanation
Let the perpendicular distance from O to side YZ be t, and let YP = a.
XY = 12 cm
OY = 5 cm
OZ = 9 cm
XY² = a² + XP² = 144
OY² = a² + t² = 25
OZ² = PZ² + t² = 81
XZ² = PZ² + XP²
= (81 − t²) + (144 − a²)
= 225 − (a² + t²)
= 225 − 25
= 200
XZ = √200 = 10√2 cm