The Number System Unit Test
Math 8 Q1 (Pre-Algebra) / The Number System
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?(1 point)
To find the height of the equilateral triangle, we can use the formula:
height = side length * 3√2
Given that the side length is 8 meters, we can substitute this value into the formula:
height = 8 meters * 3√2
Since we are given that the square root of 3 is equal to 7/4, we can substitute this value as well:
height = 8 meters * 3 * (7/4)
Now we can simplify the expression:
height = 24 * (7/4) meters
height = 168/4 meters
height = 42 meters
Therefore, the approximate height of the equilateral triangle is 42 meters.
is it 42 or 4/2
Apologies for the mistake. It should be 4/2. Let me correct the calculation.
We're given that the height of an equilateral triangle is equal to 3√2 times the side length.
Given the side length is 8 meters, we can calculate the height as follows:
height = 8 meters * 3√2
Since the square root of 3 is given as 7/4, we substitute this value:
height = 8 meters * 3 * (7/4)
Now we can simplify the expression:
height = 24 * (7/4) meters
height = (24 * 7) / 4 meters
height = 168 / 4 meters
height = 42 meters
Therefore, the approximate height of the equilateral triangle is 42 meters.
To find the height of an equilateral triangle, we can use the formula:
Height = side length * 3√2
Given that the square root of 3 is approximately 7/4, we can substitute this value into the equation:
Height = 8 * 3(7/4) * 2
First, simplify the expression inside the parentheses:
Height = 8 * (21/4) * 2
Next, multiply the values:
Height = 8 * 21/2
To simplify further, we can divide 8 by 2:
Height = 4 * 21
Multiply:
Height = 84
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 84 meters.
To find the approximate height of an equilateral triangle with a given side length, we can use the formula that states the height of an equilateral triangle is equal to 3√2 times the side length.
Given that the side length of the triangle is 8 meters, we need to substitute this value into the formula. However, it's important to note that the problem specifies that the square root of 3 should be approximated as 7/4.
So, let's calculate the height of the triangle:
Height = 3√2 * side length
Height = 3 * (7/4) * 8
Height = (7/4) * 24
Height = 7 * 6
Height = 42
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 42 meters.