Question

the area of equilateral triangle is 4 root 3 cm square what is its perimeter​

Answer 1

Answer:

Let each side of the equilateral triangle ABC be x.

Let the perpendicular from A to side BC of the triangle ABC be AY

Area of the triangle = 1/2 (base ∗∗ height)

Here Base = x/2

Height = Perpendicular AY ( as described previously)

AY 22 == AC 22 −− YC 22

= x 22 −− (x/2) 22 =(3∗x2)/4=(3∗x2)/4

So, Height of the triangle ABC = squareroot(squareroot( AY) = squareroot(3)x/2squareroot(3)x/2

Given that area of the triangle = 4 ∗squareroot(3)∗squareroot(3)

Therefore ,

4 ∗squareroot(3)∗squareroot(3) = 1/2 (base ∗∗ height)

= 1/2∗(x∗(squareroot3)∗x/2)1/2∗(x∗(squareroot3)∗x/2)

= (( x2∗squareroot3)/4x2∗squareroot3)/4

Hence,

4 ∗squareroot(3)∗squareroot(3) = (x2∗squareroot3)/4(x2∗squareroot3)/4

16 = x2x2

So x = 4

Hence each side is 4 cm

Answer 2

=>side=4cm ...........................