Question

a straight line forms a right angled triangle with axes of coordinate. the hypotenuse of the triangle is 13 units and area is 30 square units . find the equation of the straight line​

Answer 1

Answer:

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Answer 2

Triangle

A right angles triangle is formed with the axes of coordinates and hypotenuse of the triangle is $13 \ units$. The area of triangle is $30 \ units^{2}$.

The picture showing the scenario is attached.

$c=13 \ units$

We know that,

$hypotenuse^{2} =height^{2}+base^{2} \\\\\implies c^2=a^2+b^2\\\\\implies 13^2=a^2+b^2\\\\\implies 169=a^2+b^2--------------(i)$

$\frac{1}{2}\times height\times base=30 \ square\ units$

$\implies \frac{1}{2}\times a\times b=30\\ \\\implies a\times b =60---------------(ii)$

On solving both equation, we get,

$169=[\frac{60}{b}]^2+b^2\\ \\\implies 169=\frac{3600}{b^2}+b^2\\ \\\implies 169b^2=3600+b^4\\\\\implies b^4-169b^2+3600=0\\\\\implies b^2=\frac{(169\pm119)}2$

$\implies \frac{169+119}{2} =12\\and\\\implies \frac{169-119}{2}=5$

We get two values of b as 12 and 5.

Which means when b is $5$

then

$a$ will be $12$.

Hence, equation of line AB will be,

$\frac{x}{b}+ \frac{y}{a}=1\\ \\\implies \frac{x}{5} +\frac{y}{12} =1\\\\\implies 12x+5y=60$

This is the required equation of straight line.