Question

height of an eqilateral triangle is 6cm find its side?​

Answer 1

Answer:

Height of the equilateral triangle =23(side)=23x.

6=23x

x=312

x=3123=6.92cm

Now,

Area of a triangle =43(side)2=43×6.92×6.92=20.76cm2

Answer 2

Given:

An equilateral triangle with height 6 cm

To find:

Side of the triangle

Concept used:

• Pythagoras Theorem

Solution:

Before reading solution, first take a look at the figure.

First draw height of the equilateral triangle from A to BC making the height AD.

We know, AD = 6 cm. (Given)

Now let the side be of the equilateral triangle ABC be a.

Now, Consider right angled triangle ADB.

In the triangle,

AB = a,

BD = BC/2 = AB/2 = a/2,

& AD = 6 cm. (Given)

Now using Pythagoras Theorem in triangle ADB, we get:

BD² + AD² = AB²

Substituting the value of AB, BD & AD, we get:

${( \frac{a}{2} )}^{2} + {6}^{2} = {a}^{2}$

$= > \frac{ {a}^{2} }{4} + 36 = {a}^{2}$

$= > {a}^{2} - \frac{ {a}^{2} }{4} = 36$

$= > \frac{4 {a}^{2} - {a}^{2} }{4} = 36$

$= > 3 {a}^{2} = 4 \times 36$

$= > {a}^{2} = \frac{4 \times 36}{3}$

$= > {a}^{2} = 48$

$= > a = \sqrt{48}$

$= > a = 4 \sqrt{3}$

and that's the answer

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