mistake in book?

[TeachSteve]

I think I found a mistake in a book and would like a second opinion. The question is finding the area of an equilateral triangle with sides of 4 inches. The answer uses the pythagorean theorem to solve. It cuts the triangle into two right triangles each with a base of 2 and hypotenuse of 4 and solves for h by adding the square of each side getting 2 radical 5 for the height. I don't believe this is correct. I believe it should be 4^2 - 2^2 = h^2 or 2 radical 3. Can someone verify I am correct?

Thanks,

Steve

 

[tkhunny]

It happens. Assuming your description is exactly correct, I would have to agree.

\(\displaystyle 2\cdot \sqrt{5} = 4.472ish\) It's unlikely a leg of a right triangle would be greater than the hypotenuse.

 

[galactus]

The area of an equilateral triangle is \(\displaystyle A=\frac{\sqrt{3}}{4}s^{2}\), where s is the side length.

The area of the triangle of side length four is then \(\displaystyle \frac{\sqrt{3}}{4}\cdot 4^{2}=4\sqrt{3}\)

The height of an equilateral triangle is \(\displaystyle h=\frac{\sqrt{3}}{2}s\)

So, the height of your triangle would be \(\displaystyle \frac{\sqrt{3}}{2}\cdot 4=2\sqrt{3}\)

 

[Deleted member 4993]

Looks like they calculated 4[sup:3c2kpf1m]2[/sup:3c2kpf1m] + 2[sup:3c2kpf1m]2[/sup:3c2kpf1m]