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leonid [27]
3 years ago
8

Please look at the photo

Mathematics
1 answer:
Anni [7]3 years ago
3 0

We want a 30-60-90 triangle with a perimeter of 8 + 4\sqrt2. If the shorter leg has length x, we must have

x + x\sqrt3 + 2x = 8 + 4\sqrt2\\3x + x\sqrt3 = 8 + 4\sqrt2\\x(3 + \sqrt3) = 8 + 4\sqrt2\\x = \boxed{\frac{8 + 4\sqrt2}{3 + \sqrt3}}

What a mess.

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