sailorsheftal
sailorsheftal sailorsheftal
  • 21-07-2021
  • Mathematics
contestada

The triangle below is equilateral. Find the length of side x in simplest radical form
with a rational denominator.
12

The triangle below is equilateral Find the length of side x in simplest radical form with a rational denominator 12 class=

Respuesta :

wegnerkolmp2741o
wegnerkolmp2741o wegnerkolmp2741o
  • 21-07-2021

Answer:

4sqrt(3)

Step-by-step explanation:

If the triangle is equilateral, the hypotenuse is 2x

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (2x)^2

x^2 + 144 = 4x^2

144 = 4x^2 -x^2

144 = 3x^2

48 = x^2

Taking the square root of each side

sqrt(48) = sqrt(x^2)

sqrt(16*3) = x

4 sqrt(3) =x

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