How do you find the length of the third side of an equilateral triangle?

Correct answer:

1. The height splits the triangle’s base in half and creates two right triangles. Create expressions for the length of the two unknown sides in this new triangle:
2. Use the Pythagorean Theorem to find the value of or the side length:
3. Multiply the side length you found by 3 to get the perimeter:

How do you find the length of the median in an equilateral triangle?

Detailed Solution

1. Given: ΔPQR is an equilateral triangle.
2. Concept used: In an equilateral triangle,
3. Calculation: Let PS be the median of ΔPQR.
4. ∴ The length of median of an equilateral ΔPQR is (5√3)/2. Important Points.
5. In an equilateral trianlge:

How do you find the height of a triangle of an equilateral triangle?

Formula to calculate height of an equilateral triangle is given as: Height of an equilateral triangle, h = (√3/2)a, where a is the side of the equilateral triangle.

How do u know if a triangle is equilateral?

Equilateral Triangle: A triangle is said to be equilateral triangle if all the sides are equal. If X, Y, Z are three sides of the triangle. Then, the triangle is equilateral only if X = Y = Z.

How do you know if a triangle is equilateral?

A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same inradius. A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.

What is the length of an equilateral triangle?

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°….

Equilateral triangle
Area
Internal angle (degrees)	60°

Are the medians of an equilateral triangle equal?

A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .

How do you find the centroid of an equilateral triangle?

The centre of mass of the equilateral triangle is at a distance of H/3 from the centre of the base of the triangle. H is the height of the triangle. The centroid or the centre of mass divides the median in 2:1 ratio.

What is the formula of equilateral?

The student will also learn the area of equilateral triangle formula. An equilateral triangle is a triangle whose all three sides are having the same length. This is the only regular polygon with three sides….A= \frac{\sqrt{3}a^2}{4}

A	Area of Equilateral triangle
a	Side length

What is the perimeter of an equilateral triangle whose area is 12 cm?

The perimeter of an equilateral triangle is 3a. Question 1: Find the area of an equilateral triangle whose perimeter is 12 cm. As per formula: Perimeter of the equilateral triangle = 3a, where “a” is the side of the equilateral triangle. Step 1: Find the side of an equilateral triangle using perimeter. Thus, the length of side is 4 cm.

How to find the length of side of an equilateral triangle?

Step 1: Find the side of an equilateral triangle using perimeter. 3a = 12 a = 4 Thus, the length of side is 4 cm. Step 2: Find the area of an equilateral triangle using formula.

How do you find the semiperimeter of an equilateral triangle?

Semiperimeter of Equilateral Triangle: s = 3a / 2. Area of Equilateral Triangle: K = (1/4) * √3 * a 2. Altitude of Equilateral Triangle h = (1/2) * √3 * a. Angles of Equilateral Triangle: A = B = C = 60°. Sides of Equilateral Triangle: a = b = c. 1. Given the side find the perimeter, semiperimeter, area and altitude.

How do you find all the unknown values of an equilateral triangle?

For equilateral triangles h = ha = hb = hc. If you have any 1 known you can find the other 4 unknowns. So if you know the length of a side = a, or the perimeter = P, or the semiperimeter = s, or the area = K, or the altitude = h, you can calculate the other values.