The altitude of an equilateral triangle is 7 square root 3 units long. The length of one side of the triangle is ____ units.

7
14
14 square root 3
7 square root 3 over 2

To find the length of one side of the equilateral triangle, we can use the formula for the altitude of an equilateral triangle. The altitude is a line segment that runs from one vertex of the triangle to the midpoint of the opposite side and forms a right angle.

Given that the altitude is 7√3 units long, we can use this information to find the length of one side. In an equilateral triangle, the altitude bisects the base (opposite side) and forms two congruent 30-60-90 right triangles. In a 30-60-90 triangle, the sides are in a ratio of 1 : √3 : 2.

Since the altitude is the longer leg (opposite the 60-degree angle) and its length is 7√3 units, the shorter leg (opposite the 30-degree angle) is 7 units.

Thus, the length of one side of the equilateral triangle is 7 units. Therefore, the correct answer is 7 units.

To find the length of one side of an equilateral triangle when given the altitude, we need to use some properties of equilateral triangles.

In an equilateral triangle, all sides and angles are equal. The altitude of an equilateral triangle bisects the base, forming two congruent right triangles. The altitude is also a perpendicular line from one vertex to the base.

In this case, we are given that the altitude of the equilateral triangle is 7√3 units long. Let's denote the length of one side of the triangle as "x."

To find the length of one side, we can use the Pythagorean Theorem in one of the right triangles formed by the altitude and the base.

Using the Pythagorean Theorem:

(7√3)^2 = (x/2)^2 + (x)^2

Simplifying the equation:

147 = (x^2/4) + x^2

Multiplying through by 4 to eliminate the fraction:

588 = x^2 + 4x^2

588 = 5x^2

Dividing both sides by 5:

117.6 = x^2

Taking the square root of both sides:

x ≈ √117.6

x ≈ 10.83 units

Therefore, the length of one side of the equilateral triangle is approximately 10.83 units.

The altitude of an equilateral triangle is 7 units long. The length of one side of the triangle is ____ units.

Draw your right triangle. A standard 30-60-90 has legs in the ratio of height:base = √3:1

Your altitude is 7√3 so the other leg is 7.

The side of the triangle is twice the base, so 14.