In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively. N is a point on the segment LM such that LN: NM = 1 : 2. If LN = 5 cm, then YZ is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 30 cm.
LN = 5 cm, then NM = 10 cm
LM = LN + NM = 5 + 10 = 15 cm
In ΔXYZ and ΔXLM, ∠X = ∠X [Common]
∠XYZ = ∠XLM
∠XZY = ∠XML
ΔXYZ ~ ΔXLM
Now, LM/YZ = XL/XY
⇒ 15/YZ = XL/2XL = 1/2
⇒ YZ = 15 × 2 = 30 cm