Question

If the graph of the equation 4x+3y=24 cuts the x-axis at P and y-axis at Q, then hypotenuse of right triangle POQ is of length​

Answer 1

Answer:

Equation :- 4x+3y=12

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

⇒4x+3(0)=12

⇒4x=12

⇒x=3

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

⇒4(0)+3y=12

⇒3y=12

⇒y=4

If OA=3units

OB=4units

By Pythagoras theorem

(AB)

2

=(OA)

2

+(OB)

2

=(3)

2

+(4)

2

=9+16

=25

=

25

⇒AB=5units

∴ The correct option is 'C'

solution

Step-by-step explanation:

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Answer 2

Answer:

The hypotenuse of right triangle POQ is of length​ is 10 units

Step-by-step explanation:

Given: The graph of the equation 4x+3y=24 cuts the x-axis at P and y-axis at Q

To find: The length of the hypotenuse of right triangle POQ

Solution:

The graph of the equation 4x+3y=24

When the graph cuts x axis then the y coordinates becomes zero

Sub y = 0 in the given equation

⇒ 4x+3y=24

⇒  4x + 3 (0) = 24

⇒ 4x = 24

⇒  x = 6

Similarly when the graph cuts the y axis x coordinates is zero

Sub x = 0 in the given equation

⇒ 4x+3y=24

⇒  4(0) + 3y = 24

⇒ 3y = 24

⇒  y = 8

OP = 6 units

OQ = 8 units

By Pythagoras theorem

$(PQ)^{2} = (OP)^{2} + (OQ)^{2}$

         = $(6)^{2} + (8)^{2}$

         = 36 + 64

        = 100

 PQ = 10 units

Final answer:

The hypotenuse of right triangle POQ is of length​ is 10 units

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