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blsea [12.9K]
3 years ago
14

Use the Pythagorean theorem to find x, in simplest radical form

Mathematics
2 answers:
Sidana [21]3 years ago
6 0

Answer:

x = 4 \sqrt{21}

Mars2501 [29]3 years ago
4 0

Answer:

4\sqrt{21}

Step-by-step explanation:

Pythagorean theorem is a^{2} +b^{2} =c^{2}.

Which in this case:

'c' is hypotenuse. (hypotenuse = 20)

'a' and 'b' are the other sides. (a = x, b = 8)

  1. a^{2} +b^{2}= c^{2}
  2. x^{2} +8^{2} =20^{2}
  3. x^{2} + 64 = 400
  4. x^{2} = 336

Now we should just take square root from the both sides.

and the answer will be \sqrt{336} or -\sqrt{336}, but a side of a triangle can not be a negative number! so the answer will be \sqrt{336}.

As you see \sqrt{336} is not the simplest radical.

We can write \sqrt{336} as \sqrt{16 * 21}.

And from the laws of radical we can write \sqrt{16*21} as \sqrt{16} * \sqrt{21}.

\sqrt{16} * \sqrt{21} = \sqrt{16}\sqrt{21} = 4\sqrt{21}

I hope it helps you. Please choose my answer as the brainliest.

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