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 12 meters?
A.11 1/2
B. 10 1/2
C. 9 1/2
D. 10 1/4
The height of an equilateral triangle equals √3/2 times the side length.
Using 7/4 for the square root of 3, we can multiply it by 12 meters to find the approximate height of an equilateral triangle with a side length of 12 meters.
The height ≈ (7/4) * 12 = 21 meters/4 = 5.25 meters.
Therefore, the approximate height in meters of an equilateral triangle with a side length of 12 meters is 5.25 meters.
None of the given options (A, B, C, or D) matches the approximate height value.
To find the approximate height in meters of an equilateral triangle with a side length of 12 meters, we can use the formula:
Height = (√3/2) * side length
Given that √3 ≈ 7/4, we can substitute it into the formula:
Height = (7/4)(1/2) * 12
Simplifying:
Height = (7/8) * 12
Height = (7/8) * (12/1)
Height = (7 * 12) / (8 * 1)
Height = 84 / 8
Height = 10.5
Therefore, the approximate height in meters of an equilateral triangle with a side length of 12 meters is 10 1/2 meters.
The answer is B. 10 1/2.
To find the approximate height of an equilateral triangle with a side length of 12 meters, we can first calculate the value of √3/2 given that the square root of 3 is approximately 7/4.
To do this, we multiply 7/4 by 3/2:
(7/4) * (3/2) = (21/8)
Now, we can calculate the height by multiplying the side length (12 meters) by the value of √3/2:
12 * (21/8) = 252/8
Simplifying 252/8, we get:
252/8 = 31.5
Therefore, the approximate height of the equilateral triangle is 31.5 meters.
Among the given options, none of them matches exactly with the calculated height. However, the closest option is D. 10 1/4.