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What is the area of the triangle ABC?

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What is the area of the triangle ABC?

by Vincen » Mon Jan 29, 2018 3:07 am
What is the area of the triangle ABC?

(1) The edge AB of the triangle is 8 inches.

(2) Triangle ABC is equilateral

The OA is C.

How can I find the area just knowing that the triangle is equilateral? Experts, can you help me? I'd appreciate your help here.
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Source: — Data Sufficiency |

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by ErikaPrepScholar » Tue Jan 30, 2018 6:12 am
We can work through this problem really quickly if we happen to know that we can solve for the area of an equilateral triangle using:
$$A=\frac{\sqrt{3}}{4}a^2$$
where a is the length of one side of the triangle.

However, even if we don't know that, we can still solve. We know that all sides of the triangle are 8 inches long because the triangle is equilateral. envision dividing our equilateral triangle in half, giving two right triangles with a base of 4 and a hypotenuse of 8. Using the pythagorean theorem, we can then solve for the height by plugging in
$$4^2+h^2=8^2$$
$$h^2=80$$
$$h=4\sqrt{5}$$
Once we fing the height, we can then solve for the area of the equilateral triangle using
$$A=\frac{1}{2}bh$$
where b = 8:
$$A=\frac{1}{2}8*4\sqrt{5}$$
$$A=16\sqrt{5}$$
So the statements are sufficient together. Of course, we don't actually need to solve for the area, or even the height of the triangle - since this is DS, all we need to do is know that if we know the length of one side on an equilateral triangle, we can find the area and solve the problem.
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