Question

if the perimeter of an equilateral triangle is 36 CM calculate its area and height​

Answer 1

Step-by-step explanation:

The perimeter is 36cm

Hence the side of the equilateral triangle is 36/3 = 12cm.

The median of the equilateral triangle is also the altitude of the triangle.

Median bisects the third side

Hence, by Pythagoras theorem

Hypotenuse = 12cm

Base = 6cm

Altitude will be 6 route 5

Area = 1/2*base*height

36 route 5

Answer 2

We know that

Perimeter of an equilateral triangle = 3 × side

Substituting the values

36 = 3 × side

By further calculation

side = 36/3 = 12 cm

So AB = BC = CA = 12 cm

Here

Area of equilateral triangle = √3/4 (side)2

Substituting the values

= √3/4 (12)2

By further calculation

= √3/4 × 12 × 12

So we get

= √3 × 3 × 12

= 1.73 × 36

= 62.4 cm2

In triangle ABD

Using Pythagoras Theorem

AB2 = AD2 + BD2

Here BD = 12/2 = 6 cm

Substituting the values

122 = AD2 + 62

By further calculation

144 =AD2 + 36

AD2 = 144 – 36 = 108

So we get

AD = √108 = 10.4

Therefore, the required height is 10.4 cm.

${\fcolorbox{blue}{black}{\blue{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:HumanIntelligence\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$