question_answer

Area of a triangular field is \[({{x}^{4}}-6{{x}^{3}}-26{{x}^{2}}+138x-35){{m}^{2}}\]and base of the triangular field is \[({{x}^{2}}-4x+1)m\]. Find the height of the triangular field.

A)  \[2({{x}^{2}}-2x-35)m\]

B)  \[\frac{1}{2}({{x}^{2}}-2x-35)m\]

C)  \[2(3{{x}^{2}}-x-4)m\]

D)  \[\frac{1}{2}(3{{x}^{2}}-x-4)m\]

Correct Answer: A

Solution :

Base of the triangular field = \[({{x}^{2}}-4x+1)m\] Area of the triangular field \[=\frac{1}{2}\times Base\times Height\] Now, \[{{x}^{4}}-6{{x}^{3}}-26{{x}^{2}}+138x-35\]             \[\frac{1}{2}\times \left( {{x}^{2}}-4x+1 \right)\times Height\] \[\Rightarrow \]Height \[=\frac{2({{x}^{4}}-6{{x}^{3}}-26{{x}^{2}}+138x-35)}{{{x}^{2}}-4x+1}\]