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

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
$4 x + 3 y = 12 P u t y = 0 t h e n, w e g e t 4 x + 3 (0) = 12 \Rightarrow x = 3 \Rightarrow A (3, 0) P u t x = 0 t h e n, w e g e t 4 (0) + 3 y = 12 \Rightarrow y = 4 \Rightarrow B (0, 4)$

$In △ A O B, AB is the hypotenuse of the given triangle$
$The length OA = 3 units and OB = 4 units A B = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5 units$

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Similar questions

Q. If the graph (O is the origin) of the equation

4 x + 3 y = 12

cuts the coordinate axes at A and B respectively, then the length of the hypotenuse of right angle triangle AOB is :

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4 x + 3 y = 12

cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB

Q. 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 ___. (O is origin)

Q. The area of the triangle formed by the line x + 3y = 12 and the coordinate axes is
(a) 12 sq units
(b) 18 sq units
(c) 24 sq units
(d) 30 sq units

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $Δ A B C$ , if AB and BC are parallel to the coordinate axes as shown in the figure.

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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

The correct option is C 5 units4x+3y=12Put y=0 then,we get4x+3(0)=12⇒x=3⇒A(3,0)Put x=0 then, we get4(0)+3y=12⇒y=4⇒B(0,4) In △AOB, AB is the hypotenuse of the given triangle The length OA = 3 units and OB = 4 unitsAB=√32+42=√25=5 units