Question

if the line 3 X + 4 Y = p makes a triangle of area 24 square unit with the co-ordinate Axes then find the value of p​

Answer 1

Answer :

p = ± 24

Note :

• The intercept form of a line is given by ;

x/a + y/b = 1 , where a and b are the x-intercept and y-intercept respectively .

• The area of triangle formed by the line and the coordinate axes is given by ; A = ½•|ab|

Solution :

Here ,

The given equation of line is ;

3x + 4y = p

The given equation can be rewritten as ;

$= > \frac{3x}{p} + \frac{4y}{p} = 1$

$= > \frac{x}{ \frac{p}{3} } + \frac{y}{ \frac{p}{4} } = 1$

Also ,

The given area of the enclosed triangle is 24 sq. units .

Thus ,

=> ½•| (p/3)•(p/4) | = 24

=> ½•| p²/12 | = 24

=> |p²|/24 = 24

=> |p²| = 24•24

=> p² = 24•24 [ °•° |p²| = p² ]

=> p = ± √(24•24)

=> p = ± 24

Hence p = ± 24