Question

The area of the triangle formed by the co-
ordinate axes and a line is 6 sq units and the
length of hypotenuse is 5 units. Find the
equation of the line​

Answer 1

Answer:

Let the intercept made by the lime on respective axis be a and b units.

$area \: of \: triangle = 6 \\ \frac{1}{2} ab = 6 \\ so \: ab \: = 12.......(1) \\ also by \: using \: pythagoras \: theorem \\ {a}^{2} + {b}^{2} = {5}^{2} \\ {a}^{2} \: + {b}^{2} = 25 \\ {a}^{2} + {( \frac{12 }{a} )}^{2} = 25 \\ {a}^{2} + \frac{144}{ {a}^{2} } = 25 \\ {a}^{4} + 144 = 25 {a}^{2} \\ {a}^{4} - 25 {a }^{2} + 144 = 0 \\ ( {a}^{2} - 16)( {a}^{2} - 9) = 0 \\ so \: a = 4 \\ a = - 4 \\ a = 3 \\ a = - 3 \\ so \: when \: a = 4 \: then \: b = 3 \\ equation \: of \: line \: is \: \frac{x}{4} + \frac{y }{3} = 1 \\ similarly \: when \: a \: = 3 \: then \: b \: = 4 \\ equation \: of \: lime \: is \: \: \frac{x }{ - 4} + \frac{y}{ - 3} = 1 \\ similarly \: \frac{x}{3} + \frac{y}{4} = 1 \\ similarly \: \frac{x}{ - 3} + \frac{y}{ - 4} = 1$