Question

the height of an equilateral triangle is √3a units, then its side is ____units ​

Answer 1

The height of an equilateral triangle is $\sqrt{3}a$ units, then its side is 2a units.

Tips (Pythagorean theorem):

If a, b and c be the base, height and hypotenuse respectively of a right-angled triangle, then

$a^{2}+b^{2}=c^{2}$

Step-by-step explanation:

Let, x be the length of each side of the equilateral triangle.

We draw ΔABC, whose AB = BC = CA = x units.

Now, we draw a perpendicular from A on BC and name it AD (given, AD = $\sqrt{3}a$ units).

Also, BD = CD = $\dfrac{x}{2}$ units.

Since ΔABD is a right-angled triangle, then

$(AD)^{2}+(BD)^{2}=(AB)^{2}$

$\Rightarrow (\sqrt{3}a)^{2}+(\dfrac{x}{2})^{2}=x^{2}$

$\Rightarrow 3a^{2}+\dfrac{x^{2}}{4}=x^{2}$

$\Rightarrow \dfrac{3}{4}x^{2}=3a^{2}$

$\Rightarrow x^{2}=4a^{2}$

$\Rightarrow x=2a$

• since $x>0$

So, the length of a side is 2a units.

#SPJ3

Answer 2

Given:

height of the equilateral triangle , = √3a units

To Find:

Find the area of the equilateral triangle

solution:

Let there will be equilateral triangle ABC

AB = BC =CA

AD is the height = √3a units

let the side of the equilateral triangle be x

then height is given by (√3/2)x

as the height is given as √3a

so √3a =  (√3/2)x

x = 2a

Hence the side of the equilateral triangle is 2a.