Question

Altitude of an equilateral triangle is $h$ unit. Find the dimension of its side.

• A. $\frac{2}{\sqrt{3}}h$ unit
• B. $\frac{2}{3}h$ unit

Answer 1

The correct option is A $\frac{2}{\sqrt{3}}h$ unit

Let each side of the equilateral triangle is $a$ unit.

The altitude of a triangle will touch the opposite side of the vertex at the midpoint because in equilateral triangle, angle bisector, altitude and median for all sides are same.


Hence, $QS=SR=\frac{a}{2}$

Now, consider the right-angled triangle $△PQR.$

PQ is the hypoteneuse of the triangle.
$\therefore a^2=h^2+(\frac{a}{2}{)}^2$
$\Rightarrow a^2-\frac{a^2}{4}=h^2$
$\Rightarrow \frac{3}{4}{a}^2=h^2$
$\Rightarrow a^2=\frac{4}{3}{h}^2$
(takeing square root both side)
$\Rightarrow a=\frac{2}{\sqrt{3}}h$

$\therefore$ Dimension of each side of the equilateral triangle is $\frac{2}{\sqrt{3}}h$ unit.