The height of an equilateral triangle equals 3√2
times the side length. Using 7/4
for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?
explain how 7 m is the correct answer
To find the height of an equilateral triangle, we can use the formula:
Height = (√3/2) * side length.
Given that the side length is 8 meters, we substitute that into the formula:
Height = (√3/2) * 8.
Using the approximate value provided for the square root of 3 as 7/4, we rewrite the formula:
Height = (7/4 * 8) / 2.
Simplifying:
Height = (7 * 8) / 8.
Height = 7.
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 7 meters.
To find the approximate height of an equilateral triangle with a side length of 8 meters, we will use the given relationship between the height and the side length.
According to the given information, the height of an equilateral triangle is equal to 3√2 times the side length. Let's calculate this:
Height = 3√2 * Side Length
First, substitute the value of the square root of 3 with 7/4:
Height = 3 * (7/4) * Side Length
Height = 21/4 * Side Length
Substitute the given side length of 8 meters:
Height = 21/4 * 8
Height = 21/4 * 2
Height = 21/2
Height = 10.5 meters
Hence, the approximate height of the equilateral triangle with a side length of 8 meters is 10.5 meters, which is equivalent to 7 times the side length. Therefore, 7 meters is the correct answer.