The area of an equilatoral triangle ABC is 50cm^2 . Find AB.
Area = (1/2)*base*(base/2)*sqrt3
= (sqrt3)(base)^2/4 = 50
base^2 = 200/sqrt3 = 115.47
base = 10.7456599
All sides have that length, since the triangle is equilateral.
Why did the equilateral triangle go to school?
To see if it could find its side A-B-C!
To find the length of side AB of an equilateral triangle, we need to use the formula for the area of an equilateral triangle.
The formula for the area of an equilateral triangle is: A = (√3/4) * s^2, where A is the area and s is the length of each side.
Let's substitute the given area into the formula and solve for s:
50 = (√3/4) * s^2
First, we will multiply both sides of the equation by 4/√3 to isolate s^2:
50 * (4/√3) = s^2
Now, let's simplify the left side of the equation:
200/√3 = s^2
To solve for s, we will take the square root of both sides:
√(200/√3) = √(s^2)
Simplifying further:
√(200/√3) = s
Calculating:
s ≈ 8.16 cm
Therefore, the length of side AB is approximately 8.16 cm.
To find the length AB of an equilateral triangle, we need to use the formula for the area of an equilateral triangle.
The formula for the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * (side length)^2
Here, we are given that the area of the triangle is 50 cm^2. Let's substitute this value into the formula:
50 = (sqrt(3) / 4) * (side length)^2
To solve for the side length, we can rearrange the equation:
(side length)^2 = (50 * 4) / sqrt(3)
(side length)^2 = 200 / sqrt(3)
Now, we can take the square root of both sides to find the value of the side length:
side length = sqrt(200 / sqrt(3))
Calculating this value using a calculator, we find:
side length ≈ 12.91 cm
Since an equilateral triangle has all sides of equal length, AB will also be equal to this side length.
Therefore, AB ≈ 12.91 cm.
We know all angles are 60° and all sides are equal.
Let the side be x cm
(1/2)(x)(x)sin60° = 50
x^2 = 100/(√3/2) = 200/√3
x = 10√2/(√√3)) = appr. 10.75 cm
or let each side be 2x
then the height is √3 x
area = (1/2)(2x)(√3x) = 50
√3x^2 = 50
x^2 = 50/√3
x = 5.3728 appr.
so 2x, the side is appr. 10.75