An equilateral triangle has an altitude of 15m. What is the perimeter of the triangle. Could someone please explain how to find perimeter. I believe the answer to be 60 sq rt 3m
30 sq rt 3
I still don't get nor understand how you guys got your answer help me please!
To find the perimeter of an equilateral triangle, you need to know the length of one side.
In this case, the altitude of the triangle is given as 15m.
Since the triangle is equilateral, the altitude will also be the height of the triangle, dividing it into two congruent right triangles.
Using the Pythagorean theorem, we can find the length of one side of the triangle.
Let's denote the length of one side of the equilateral triangle as "s". The altitude divides the equilateral triangle into two congruent right triangles, and we can label the base of one of these right triangles as "b".
According to the Pythagorean theorem, we have:
b^2 + (s/2)^2 = s^2
Substituting the given value of the altitude, we have:
15^2 + (s/2)^2 = s^2
225 + (s^2/4) = s^2
Multiplying both sides by 4 to remove the fraction, we get:
900 + s^2 = 4s^2
Rearranging the terms, we have:
3s^2 = 900
Dividing both sides by 3, we get:
s^2 = 300
Taking the square root of both sides, we get:
s = √300
Simplifying the square root, we have:
s = √(100 * 3)
s = 10√3
Now that we have the length of one side, we can determine the perimeter of the equilateral triangle.
The perimeter of an equilateral triangle is equal to three times the length of one side. Therefore, the perimeter is:
Perimeter = 3s
Perimeter = 3 * (10√3)
Perimeter = 30√3
So, the perimeter of the equilateral triangle is 30√3 meters.
To find the perimeter of an equilateral triangle, we need to know the length of one side.
In this case, we know that the triangle has an altitude of 15m. An altitude of an equilateral triangle splits the triangle into two congruent right-angled triangles. Since the given altitude is perpendicular to the base (a side of the triangle), each of the two right-angled triangles formed is a 30-60-90 triangle.
In a 30-60-90 triangle, the ratio of the sides is as follows:
- The side opposite the 30-degree angle is half the length of the hypotenuse.
- The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
- The hypotenuse (which is also the base of the equilateral triangle) is twice the length of the side opposite the 30-degree angle.
Since the altitude of the equilateral triangle is 15m, we can determine that the side opposite the 30-degree angle in each of the right-angled triangles is 15m.
Using the properties of the 30-60-90 triangle, we can then calculate the length of the hypotenuse/base, which is also the side length of the equilateral triangle.
- The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
- Therefore, the side opposite the 60-degree angle is √3 * 15m = 15√3 m.
- The hypotenuse/base (which is also the side length of the equilateral triangle) is twice the length of the side opposite the 30-degree angle.
- Therefore, the hypotenuse/base is 2 * 15m = 30m.
Since the perimeter of an equilateral triangle is the sum of its three sides, we can find the perimeter by multiplying the length of one side by 3:
Perimeter = 3 * 30m = 90m.
Therefore, the perimeter of the equilateral triangle is 90m. The answer of 60√3m (approximately 103.92m) is not correct.