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A side of one equilateral triangle is congruent to an altitude of another equilateral triangle.  What is the ratio of their areas?

 Jun 12, 2020
 #1
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for example the are 1 and x for the first one we get \(\cfrac{\sqrt3}{4}\)for the first area and for the height of the other triangle we have \(\dfrac{2}{\sqrt3}\) for the base and 1 for the height so the ratio is \(\dfrac{\sqrt3}{4}\) \(:\) \(\dfrac{2}{\sqrt3}\)

 Jun 12, 2020
 #2
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Wouldn't that ratio simplify to 3/8?

Ziggy  Jun 12, 2020
 #3
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A side of one equilateral triangle is congruent to an altitude of another equilateral triangle.  What is the ratio of their areas?

 

1st Δ        side = 1        height = 0.866025403         area = 0.433012701 u²

 

2nd  Δ        height = 1          side = 1.154700538       area = 0.577350269 u²

 

The ratio of their areas is  3/4  smiley

 Jun 12, 2020

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