Question

In a triangle ABC,the altitude from A is not less than BC and the altitude from B is not less than AC.The triangle is

• A. right angled
• B. isosceles
• C. obtuse angled
• D. equilateral

Answer 1

The correct option is A right angled

In any triangle $p_1=\frac{2△}{a}$ and $p_2=\frac{2△}{b}$
given that $p_1\ge a$ and $p_2\ge b$
$\Rightarrow p_1{p}_2\ge ab$
$\Rightarrow 4\frac{{△}^2}{ab}\ge ab$
$\Rightarrow {4△}^2\ge {\left(ab\right)}^2$
$\Rightarrow 4{\left(\frac{ab\sin C}{2}\right)}^2\ge {\left(ab\right)}^2$
$\Rightarrow {\sin }^{2}C\ge 1$
Since, ${\sin }^{2}C\le 1$
Therefore, ${\sin }^{2}C=1\Rightarrow C=\frac{\pi }{2}$