Question

Drawn from origin are two mutually perpendicular straight lines forming an isosceles triangle together triangle between together with straight line $x+y=a.$ then the area of the triangle is in terms of ${}^{\prime }{a}^{\prime }?$

Answer 1

Length of perpendicular on the line $2x+y=a$ from the origin is

$L=\left|a\right|/\sqrt{5}$

We know that in right angle triangle mid point of hypotenuses is outdistance from all the vertex$.$

So area $\frac{1}{2}\times L\times 2L$

$=L^2=a^2/5.$