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# geometry

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The altitude of an equilateral triangle is the square root of 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

Sep 29, 2020

#1
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The altitude of an equilateral triangle is the square root of 3 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

Hello Guest!

$$A=\frac{1}{2}ah$$

$$h=\sqrt{3}$$

$$a^2=(\frac{a}{2})^2+h^2\\ a^2-\frac{a^2}{4}=h^2$$

$$\frac{3}{4}a^2=3\\ a=\sqrt{\frac{3\cdot 4}{3}}$$

$$a=2$$

$$A=\frac{1}{2}ah$$

$$A=\frac{1}{2}\cdot 2\cdot \sqrt{3}$$

$$A=\sqrt{3}$$ !

Sep 29, 2020
#2
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You lost me on this one, asinus.....

can you explain this step? :

a^2 = (a/2)^2 + h^2         won't that just give you the side length and not the base length?

Seems to me that we need more info to solve this Q Sep 29, 2020
#3
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SORRY .... I see your answer method now !   I read the question incorrectly as an isosceles triangle rather than equilateral triangle ....     D'Oh !

ElectricPavlov  Sep 29, 2020
edited by ElectricPavlov  Sep 29, 2020