question_answer

If the graph of the equation \[4x+3y=12\] cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length

A)  4 units                         

B)  3 units 

C)  5 units             

D)         None of these   

Correct Answer: C

Solution :

Put \[x=0\]in \[4x+3y=12,\]we get \[4\times 0+3y=12\Rightarrow y=4.\] Put y = 0 in \[4x+3y=12,\]we get \[4x+3\times 0=12\,\,\Rightarrow x=3.\] So, OB = 4 units and OA = 3 units. Now, in \[\Delta \Alpha {\mathrm O}\Beta ,\]by Pythagoras theorem \[A{{B}^{2}}=O{{B}^{2}}+O{{A}^{2}}\Rightarrow A{{B}^{2}}={{4}^{2}}+{{3}^{2}}\] \[\Rightarrow \]\[A{{B}^{2}}=16+9\Rightarrow AB=\sqrt{25}=5\] Hence, hypotenuse = 5 units.