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 ?
Answer & explanation
Correct answer: option 4
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.