question_answer

Find the length of the Longest side of the triangle formed by the line \[3x+4y=12\] with the coordinate axes:

A) 9

B) 16

C) 5

D) 7

Correct Answer: C

Solution :

[c] The graph of given linear equation is shown below:

Here, vertices of the triangle formed are \[(4,0),\]\[(0,3)\]and \[(0,0)\]. Clearly, the longest side is the hypotenuse joining \[(4,0)\] and \[(0,3)\].

It length \[=\sqrt{{{4}^{2}}+{{3}^{2}}}\]

[By Pythagoras Theorem]

\[=\sqrt{16+9}=\sqrt{25}=5\] units,