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# help

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An equilateral triangle has an area of $$64\sqrt{3}$$ $$\text{cm}^2$$. If each side of the triangle is decreased by 4 cm, by how many square centimeters is the area decreased?

Jun 22, 2019

#1
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The area of an equilateral triangle is given by $$\frac{\sqrt{3}}{4}s^2$$, where $$s$$ is the side length of the equilateral triangle. Consequently, setting this formula and expression equal to $$64\sqrt{3}$$, we get $$s^2=256$$, and $$s=16$$ centimeters. Since each side of the triangle decreases by four centimeters, the new side length of the equilateral triangle is twelve centimeters. Thus, the new area is $$36\sqrt{3}$$ centimeters, and it has decreased by $$64\sqrt{3}-36\sqrt{3}=\boxed{28\sqrt{3}}$$centimeters.

-tertre

Jun 22, 2019
#2
+7763
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$$\text{Let }l \text{ cm be the side length of the equilateral triangle.}\\ \dfrac{\sqrt3}{4} l^2 = 64\sqrt3\\ l^2 = 256\\ l = 16\\ \text{New length} = 12\text{ cm}\\ \text{New area} = \dfrac{\sqrt3}{4} (12^2) = 36\sqrt3\text{ cm}^2\\ \text{Area decrease} = 64\sqrt3 - 36\sqrt3= 28\sqrt3\text{ cm}^2$$

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Jun 22, 2019