Hello, I was having trouble solving a problem. It starts with Let F/60 be the height of an equilateral triangle and let K be the area of the triangle. Find K(sqaure root of 3) divided by 2 when F=720 This is an extra credit problem. I am having difficulty with all the problems this month. I would appreiciate any help. Thank you, Irene
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NCTM December 2010 Calendar
- Thread starter irene12
- Start date
Airless_wing
New member
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- Dec 21, 2010
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xsqrt(3)/2
When you say "K(square root of 3) divided by 2" is the equation above what you mean, if x is substituted for K? If so, then you should remember that area (K) is equal to 1/2(base)(height), and you are given the height, which is 12. That leaves two variables, K, which we what to find, and then the base of the triangle. Because it is an equilateral triangle, we know that the height and the base are related: multiply half of the base by square root of 3. Oh wait! That's already given to us in the problem! Just set xsqrt(3)/2 = 12 and solve.
This is my best guess at the solution. I is my first time working with math via the computer, so I might have misinterpreted the information, but i hope it helps
When you say "K(square root of 3) divided by 2" is the equation above what you mean, if x is substituted for K? If so, then you should remember that area (K) is equal to 1/2(base)(height), and you are given the height, which is 12. That leaves two variables, K, which we what to find, and then the base of the triangle. Because it is an equilateral triangle, we know that the height and the base are related: multiply half of the base by square root of 3. Oh wait! That's already given to us in the problem! Just set xsqrt(3)/2 = 12 and solve.
This is my best guess at the solution. I is my first time working with math via the computer, so I might have misinterpreted the information, but i hope it helps
One way to look at it:
The height of an equilateral triangle is \(\displaystyle h=\frac{\sqrt{3}}{2}s\). Where s is the side length.
Thus, \(\displaystyle \frac{F}{60}=\frac{\sqrt{3}}{2}s\). Where F is given and s can be found.
The area is given by \(\displaystyle K=\frac{\sqrt{3}}{4}s^{2}\)
Now, finish by finding \(\displaystyle K\cdot \frac{\sqrt{3}}{2}\).
The height of an equilateral triangle is \(\displaystyle h=\frac{\sqrt{3}}{2}s\). Where s is the side length.
Thus, \(\displaystyle \frac{F}{60}=\frac{\sqrt{3}}{2}s\). Where F is given and s can be found.
The area is given by \(\displaystyle K=\frac{\sqrt{3}}{4}s^{2}\)
Now, finish by finding \(\displaystyle K\cdot \frac{\sqrt{3}}{2}\).