Question about an equilateral triangle with side 20

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Alicia

July 26, 2017 04:21

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.

Yangi maqola

1 sharh

Pei-Hsin Lin 林培心 🌸

July 26, 2017 06:18

O’zgartirildi
1

Sharhlar bilan harakatlar Doimiy havola
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

Mqola sharhlar uchun yopiq

Question about an equilateral triangle with side 20

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