Question

If the graph (O is the origin) of the equation $4x+3y=12$ cuts the coordinate axes at A and B respectively, then the length of the hypotenuse of right angle triangle AOB is :

• A. 2 units
• B. 3 units
• C. 4 units
• D. 5 units

Answer 1

The correct option is D 5 units


$4x+3y=12$
for y = 0 , $x=\frac{12}{4}=3$
for x = 0 , $y=\frac{12}{3}=4$

A(3,0) cuts the x -axis
B(0,4) cuts the y-axis.

In for triangle AOB,
OA = 3 units , OB = 4 units

By Pythagorus theorem,
$AB=\sqrt{O{A}^2+O{B}^2}$
$AB=\sqrt{3^2+4^2}=5$ units