Question

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

Answer 1

hypotenuse of right triangle AOB is  5 units of length

Step-by-step explanation:

the graph of the equation 4x+3y=12 cuts the coordinate axes at A and B,

x = 0  => 4 * 0 + 3y = 12

=> y = 4

A = ( 0 , 4)

y = 0  => 4 *x  + 3* 0 = 12

=> x = 3

=> B = ( 3, 0)

AB = √(3 - 0)² + (0 - 4)²

= √9 + 16

= √25

= 5

hypotenuse of right triangle AOB is  5 units of length

or AO = 4  & BO = 3

AB² = AO² + BO²

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

the graph of the equation 4x+3y=12 cuts the coordinate axes at A and B,

x = 0 => 4 * 0 + 3y = 12

=> y = 4

A = ( 0 , 4)

y = 0 => 4 *x + 3* 0 = 12

=> x = 3

=> B = ( 3, 0)

AB = √(3 - 0)² + (0 - 4)²

= √9 + 16

= √25

= 5

hypotenuse of right triangle AOB is 5 units of length

or AO = 4 & BO = 3

AB² = AO² + BO²