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

4 units

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3 units

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5 units

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None of these

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Solution

The correct option is C 5 units
$4 x + 3 y = 12 P u t y = 0 t h e n, w e g e t 4 x + 3 (0) = 12 \Rightarrow x = 3 ∴ A (3, 0) c u t s t h e x - a x i s P u t x = 0 t h e n, w e g e t 4 (0) + 3 y = 12 \Rightarrow y = 4 ∴ B (0, 4) c u t s t h e y - a x i s$

$I n △ A O B, AB is the hypotenuse of the given triangle. T h e l e n g t h O A = 3 u n i t s a n d O B = 4 u n i t s B y p y t h o g o r a s t h e o r e m, A B = \sqrt{O A^{2} + O B^{2}} = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5 u n i t s$

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4 x + 3 y = 12

4 x + 3 y = 12

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

4 x + 3 y = 12

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