Question

area of a equilateral triangle =4√3cm² what will be the length of each side​

Answer 1

Answer:

answer is 4

Step-by-step explanation:

side =4

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 2 = AC 2 − YC 2

= x 2 − (x/2) 2 =(3∗x2)/4

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

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

Therefore ,

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

= 1/2∗(x∗(squareroot3)∗x/2)

= ( x2∗squareroot3)/4

Hence,

4 ∗squareroot(3) = (x2∗squareroot3)/4

16 = x2

So x = 4

Hence each side is 4 cm