Question : In $ riangle X Y Z$, 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:
Option 1: 30 cm
Option 2: 24 cm
Option 3: 28 cm
Option 4: 26 cm

Question

Question : In $ riangle X Y Z$, 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:

Option 1: 30 cm

Option 2: 24 cm

Option 3: 28 cm

Option 4: 26 cm

Team Careers360 · Accepted Answer

Correct Answer: 30 cm

Solution :
In ΔXYZ, L and M are the middle points of the sides XY and XZ, respectively.
LN : NM = 1 : 2 and
LN = 5 cm
In $ riangle$XYZ and in $ riangle$XLM
$\angle$X = $\angle$X [common]
$\angle$XYZ = $\angle$XLM
$\angle$XZY = $\angle$XML
$ herefore riangle$XYZ ~ $ riangle$XLM
LN : NM = 1 : 2
LN = 5 cm
$\frac{ ext{LN}}{ ext{NM}} = \frac{1}{2}$
$⇒\frac{5}{ ext{NM}} = \frac{1}{2}$
$⇒ ext{NM} = 10$ cm
LM = LN + NM = 5 + 10 = 15 cm
Since, $ riangle$XYZ ~ $ riangle$XLM
$\frac{ ext{LM}}{ ext{YZ}}=\frac{ ext{XL}}{ ext{XY}}$
$⇒\frac{15}{ ext{YZ}}=\frac{ ext{XL}}{ ext{2XL}}$ [∵ L is midpoint of XY]
$⇒\frac{15}{ ext{YZ}}=\frac{1}{2}$
$ herefore ext{YZ} = 30$ cm
Hence, the correct answer is 30 cm.

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Question : In △XYZ, 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:Option 1: 30 cmOption 2: 24 cmOption 3: 28 cmOption 4: 26 cm

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Question : In $△ X Y Z$ , 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:
Option 1: 30 cm
Option 2: 24 cm
Option 3: 28 cm
Option 4: 26 cm