Question
Solve the following examples.
Find the height of an equilateral triangle having side 2a.
Find the height of an equilateral triangle having side 2a.
✓
Answer
Let ABC be an equilateral triangle,
Let AP be a perpendicular on side BC from A.
To find : Height of triangle = AP
As, ABC is an equilateral triangle we have
AB = BC = CA = 2a
Also, we know that Perpendicular from a vertex to corresponding side in an equilateral triangle bisects the side
$\Rightarrow BP = CP =\frac{1}{2} = 'a'$
Now, In ΔABP, By Pythagoras theorem
$\text { (Hypotenuse }^2=(\text { base })^2+(\text { Perpendicular })^2$
$\Rightarrow A B^2=B P^2+A P^2$
$\Rightarrow(2 a)^2=a^2+A P^2$
$\Rightarrow A P^2=4 a^2-a^2$
$\Rightarrow A P^2=3 a^2$
$\Rightarrow A P=a \sqrt{3}$
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