In ΔXYZ, ∠Y=90 degree and YN is perpendicular to XZ. If XY = 30 cm and XZ = 34 cm, then what is the value of YN ?

(240/17) cm

In triangle XYZ, we have a right angle at Y. Therefore, using the Pyhtagoras theorem, we have

\( {XY }^{2 } \) + \( {YZ }^{2 } \) = \( { XZ}^{2 } \)

Substituting the given values, we get

\( {30 }^{2 } \) + \( {YZ }^{2 } \) = \( { 34}^{2 } \)

900 + \( {YZ }^{2 } \) = 1156

Subtracting 900 from both ides, we get

\( {YZ }^{2 } \) = 256

Taking the square root of both sides, we get,

YZ = 16

Using the area of the right angle triangle

\(\frac{1}{2}\) x 16 x 30 = \(\frac{1}{2}\) x YN x 34

YN = \(\frac{240}{17}\) cm.

Therefore, YN is \(\frac{240}{17}\) cm.