Question

if the graph of the equation 4x +3y=12 cuts the coordinate azis at A and B , then what is length of the hypotenuse of right angled triangle AOB

Answer 1

Put x = 0 we have 3y = 12 
=> y =4

Put y = 0 we have 4x = 12
=> x = 3 

Hence points  on the line are (0,4),(3,0)


Now we have to find AB

By pytha theorem

 (OA)^2 + (OB)^2 = (AB)^2
(3)^2 + (4)^2 = (AB)^2
(AB)^2 = 9+16
AB = ROOT 25
AB = 5 UNITS


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Answer 2

Answer:

5 units is the required length of the hypotenuse .

Step-by-step explanation:

Explanation:

Given ,  an equation  4x + 3y = 12

which cut the coordinate axis at A and B .

But , we know when the graph cut  x - axis  then the coordinate of y becomes zero  and  when the graph cut y- axis then the coordinate of x becomes zero.

Step 1:

Given equation is 4x + 3y = 12,

put x =0 in the equation we get ,

4 × 0 + 3y = 12

⇒3y = 12

⇒ y = 4 .

So, coordinate of B is (0,4 )

Similarly , when we put y = 0 we get ,

4x + 3 × 0 = 12

⇒4x = 12

⇒x = $\frac{12}{4}$ = 3

∴Coordinate of A is (3 , 0).

Step 2:

AOB  is a right angled  triangle in which , OA = 3 units and OB = 4 unit s

Now , by Pythagoras theorem

$AB^2 = OA^2 + OB^2$

⇒$AB^2 = 3^2 + 4^2$

⇒AB = $\sqrt{9 + 16 } = \sqrt{25}$

⇒AB = 5units

Final answer :

Hence , the length of the hypotenuse of right angles triangle is 5units .

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