wbricker3 wrote:
The area of an equilateral triangle with side length x is the same as the surface area of a cube with edge length z. If both x and z are integers, then what is x^2 in terms of z^2 ?
A. Z^2 (6√3)
B. Z^2 (8√3)
C. 72 Z^2
D. Z^2 (72√3)
E. 192 Z^2
Can anyone help explain?
Formula for Area of equilateral triangle with side \(x = \frac{x^2 \sqrt{3}}{4}\)
Formula for Surface area of cube with edge length \(z = 6z^2\)
Given Area of equilateral triangle and Surface area of cube are equal. Therefore,
\(\frac{x^2 \sqrt{3}}{4} = 6z^2\)
\(x^2 = \frac{(z^2)(6 * 4) }{\sqrt{3}}\)
\(x^2 = \frac{(z^2)(6 * 4)(\sqrt{3})}{\sqrt{3}*\sqrt{3}}\) --------- (Multiplying numerator and denominator by \(\sqrt{3}\))
\(x^2 = \frac{(z^2)(6 * 4)(\sqrt{3})}{3}\)
\(x^2 = (z^2)(2 * 4) (\sqrt{3})\)
\(x^2 = (z^2)(8 \sqrt{3})\)
Answer (B)... I am also getting answer as B...
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