Two mutually perpendicular straight lines are drawn from the origin forming an isosceles triangle together with the straight line, 2 x+y=a. Then the area of the triangle is :

Question

Two mutually perpendicular straight lines are drawn from the origin forming an isosceles triangle together with the straight line, 2 x+y=a. Then the area of the triangle is : (A) (a2/2) (B) (a2/3) (C) (a2/5) (D) none

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2bfde33356f6eaec60a936eb263a92fa-.png" /> p=|(0+0-a/√5)|=(a/√5) tan 45°=(p/x) ⇒ p=x Hence area =(1/2)(2 x)(p)=p x=p2=a2 / 5

Q. Two mutually perpendicular straight lines are drawn from the origin forming an isosceles triangle together with the straight line, $2 x + y = a$ . Then the area of the triangle is :

$\frac{a ^{2}}{2}$

$\frac{a ^{2}}{3}$

$\frac{a ^{2}}{5}$

none

$p = ∣ ∣ \frac{0 + 0 - a}{5} ∣ ∣ = \frac{a}{5}$
$tan 4 5^{\circ} = \frac{p}{x} \Rightarrow p = x$
Hence area $= \frac{1}{2} (2 x) (p) = p x = p^{2} = a^{2} /5$

Q. Two mutually perpendicular straight lines are drawn from the origin forming an isosceles triangle together with the straight line, 2x+y=a. Then the area of the triangle is :

2a2​

3a2​

5a2​