Question about an equilateral triangle with side 20

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Alicia

2017. július 26. 4:21

In one of my worksheets, I encountered an equilateral triangle with a sides == to 20. In addition, it was given with a height of 12, and I'm curious about whether this triangle is at all possible? When split into two 30-60-90 triangles, it has the sides:

hypotenuse = 20

base = 10

height = 12

which don't satisfy the Pythagorean theorem despite being a right angled triangle (100+144 =/= 400). I tried to solve a problem involving this triangle using trig functions and my answer came out wrong, so I'm wondering whether this is a valid given or if I'm missing something.

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Pei-Hsin Lin 林培心 🌸

2017. július 26. 6:18

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You're right! This problem is overdetermined. Some of the information (i.e., constraints) given are physically contradictory. The height of an equilateral triangle with sides of 20 units must be 10√3 units, not 12 units, because of the Pythagorean Theorem:

a² + b² = c²

10² + (10√3)² = 20²

100 + 300 = 400 △

Alternately, if the height really is 12 units and the base is still 20 units, then you have an isosceles triangle, with two sides that are 2√61 units, again because of the Pythagorean Theorem:

10² + 12² = (2√61)²

100 + 144 = 4(61) = 244 Δ

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Question about an equilateral triangle with side 20

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