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 multiply the side length by √3/2. Given that the square root of 3 is approximately 7/4 (as stated in the problem), we can substitute this value into the equation.
Height = (√3/2) * side length
Height ≈ (7/4) * 8
Height ≈ 7/2 * 8
Now, when we simplify this expression, we get:
Height ≈ 7 * 4
Height ≈ 28
Therefore, the approximate height in meters of an equilateral triangle with a side length of 8 meters is 28 meters.
To find the approximate height of an equilateral triangle with a side length of 8 meters, we can use the formula you provided: height = (√3/2) * side length.
First, let's calculate the square root of 3 using the given approximation of 7/4. We have:
√3 ≈ 7/4
Next, we substitute this value into the formula:
height = (7/4 * 1/2) * 8
Simplifying the expression inside the parentheses:
height = 7/8 * 8
Canceling out the 8:
height = 7/1
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 7 meters.