The length of each of the of the third side is 2x. Its perimeter is 36 centimeters. Draw and label this triangle. Write an equation that could be used to find the value of x. Solve for x and then

Answer 1

If this is an equilateral triangle, all 3 angles are equal and all 3 sides are equal.

If a side = 2x then the perimeter is 3 times 2x = 6x = 36 centimeters

6x=36

x=6

2x=12. Each side is 12 centimeters.

To find the area, put the triangle on one side, and drop a vertical line from the top to the base

That line cuts the base into two parts, each 6 centimeters.

You now have 2 right triangles, each with base 6 and height the same. The right triangles have angles 60, 30 and 90. the height is h, base is 6, and hypotenuse is 12. h^2=12^2-6^2=144-36=108

h=square root of 108. Area of each right triangle is 1/2 times 6 times square root of 108 =3sqr108

The area of both right triangles is 6sqr108 = approximately 6(10.4)=62.4 square centimeters= area of the original triangle.

Or use Heron's formula:

calculate half the perimeter: 36/2=18 subtract a side from 18: 18-12=6

multiply 18(6)(6)(6)= 18(36)6=648(6)=3888

take the square root

of 3888 = 62.4 square inches

In general for any equilateral triangle with side = s, the perimeter is 3s and the area is half side s times height of (sqr3)s

(1/4)(sqr3)s^2

or

using heron's formula sqr[(3s/2)(3s/2-s)(3s/2-s)(3s/2-s)= (3s/2-s)sqr(3s/2)(3s/2-s)

= (s/2)sqr(3s/2)(s/2)=(s/2)(s/2)sqr(3)=(s/2)^2sqr(3)

In this problem s=12, plug that into the above to get (12/2)^2 sqr(3) = 36 x 1.732 = 62.4 square centimeters

s=the perimeter divided by 3 or 36/3=12