Question

if the perimeter of an equilateral is 24 cm then find its height and area​

Answer 1

The perimeter of an Equilateral is = 24cm.

In Equilateral (a=b=c).

Now,

a+b+c = perimitre

a+a+a = 24

3a = 24

a = 24÷3 = 8cm

a=b=c=8

Now The *S* = perimitre / 2

= 24/2 = 12cm

Area of Equilateral :

=> √s(s-a)(s-b)(s-c) [ under Root ]

=> √12 (12-8) (12-8 ) (12-8 )

=> √12 × 4 × 4 × 4

=> √3×2×2×4×4×2×2

=> 2×4×2√3

=> 16√3 cm^2 Ans..

Answer 2

Answer:

16√3 cm², 4√3 cm

Step-by-step explanation:

Perimeter (a+b+c) = 24

Now, Semiperimeter (s) = 24/2 = 2 cm.

So, area of eq. triangle

$= \sqrt{s(s-a)(s-b)(s-c)}\\\\= \sqrt{12(12-8)(12-8)(12-8)}\\\\= \sqrt{12 \times 4 \times 4 \times 4}\\\\= 4 \times \sqrt{3 \times 4 \times 4}\\\\= 4 \times 4 \times \sqrt{3}\\\\= 16\sqrt{3} \: cm^2$

But, Area of triangle = = (1/2)a*h

So, 1*8*h/2 = 16√3

Or, h = (16√3 * 2)/8 = 4√3 cm