Question

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

• A. $4$ units
• B. $3$ units
• C. $5$ units
• D. None of these

Answer 1

Answer: (C)

$5$ units

Equation :- $4x+3y=12$

When the graph cuts x-axis, y coordinate becomes zero.

$\Rightarrow 4x+3\left(0\right)=12$

$\Rightarrow 4x=12$

$\Rightarrow x=3$

Similarly, when the graph cuts the y-axis, x coordinate is zero.

$\Rightarrow 4\left(0\right)+3y=12$

$\Rightarrow 3y=12$

$\Rightarrow y=4$

If $OA=3units$

$OB=4units$

By Pythagoras theorem

$(AB{)}^2=(OA{)}^2+(OB{)}^2$

$=(3{)}^2+(4{)}^2$

$=9+16$

$=25$

$=\sqrt{25}$

$\Rightarrow AB=5units$

$\therefore$ The correct option is 'C'