An equilateral triangle has side lengths of 7 inches. What is the height of the triangle? Round your answer to the nearest hundredth.
3.5 inches-
7 inches



Answer :

To find the height of an equilateral triangle with side lengths of 7 inches, you can use the formula specifically for the height of an equilateral triangle, which is derived from the Pythagorean theorem. The formula is:

[tex]\[ h = \frac{a \sqrt{3}}{2} \][/tex]

where [tex]\(a\)[/tex] is the length of a side of the triangle.

Let's walk through the steps to find the height:

1. Identify the side length: The side length [tex]\(a\)[/tex] of the equilateral triangle is given as 7 inches.

2. Apply the formula:
[tex]\[ h = \frac{7 \cdot \sqrt{3}}{2} \][/tex]

3. Calculate the height: Substitute the values into the formula and calculate the height.
[tex]\[ h = \frac{7 \cdot \sqrt{3}}{2} \approx \frac{7 \cdot 1.732}{2} \][/tex]
Doing the multiplication first:
[tex]\[ 7 \cdot 1.732 \approx 12.124 \][/tex]
Then divide by 2:
[tex]\[ \frac{12.124}{2} \approx 6.062 \][/tex]

4. Round the height to the nearest hundredth: The calculated height is approximately 6.062. When rounded to the nearest hundredth, the height is 6.06.

Thus, the height of the equilateral triangle with side lengths of 7 inches is approximately [tex]\(6.06\)[/tex] inches.