The formula for the height,h, of an equilateral triangle is h= √3/2s, where s is the length of the following
A.In terms of the length of a side,s, only
B. In terms of the height,h only
a = sh/2 = s(√3/2s)/2 = √3/4 s^2
h = √3/2 s, so s = 2h/√3
a = sh/2 = 2h/√3 * h/2 = h^2/√3
A. In terms of the length of a side, s only:
To express the height in terms of the length of a side, we rearrange the formula to solve for s.
Starting with the formula: h = √(3/2)s
We multiply both sides of the equation by 2/√3 (reciprocal of √(3/2)) to isolate s:
s = h(2/√3)
Therefore, in terms of the length of a side, s = h(2/√3).
B. In terms of the height, h only:
To express the length of the side in terms of the height, we rearrange the formula to solve for h.
Starting with the formula: h = √(3/2)s
We square both sides of the equation to isolate s:
h^2 = (3/2)s
Now, we multiply both sides of the equation by 2/3 to solve for s:
s = (2/3)h^2
Therefore, in terms of the height, h = (2/3)h^2.
A. To express the height of an equilateral triangle in terms of the length of a side, s, we can use the formula h = √3/2s.
B. To express the height of an equilateral triangle in terms of the height, h, only, we need to rearrange the formula.
Starting with the formula h = √3/2s, let's isolate s:
1. Multiply both sides of the equation by 2 to get rid of the fraction: 2h = √3s.
2. Square both sides of the equation to eliminate the square root: (2h)^2 = (√3s)^2.
3. Simplify: 4h^2 = 3s.
Now, we can express the length of the side, s, in terms of the height, h:
4. Divide both sides of the equation by 3: s = 4h^2 / 3.
Therefore, the formula for the length of the side, s, in terms of the height, h, is s = 4h^2 / 3.