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Alecsey [184]
3 years ago
6

For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified, radical

form.

Mathematics
1 answer:
sleet_krkn [62]3 years ago
6 0

Answer: c=4\sqrt{2}

Step-by-step explanation:

For this exercise you need to apply the Pythagorean Theorem. This is:

h^2=l^2+m^2

Where "h" is the hypotenuse of the Right triangle and "l" and "m" are the legs.

In this case, you can identify that:

h=c\\\\l=a=4\\\\m=b=4

Knowing these values, you can substitute them into  h^2=l^2+m^2:

c^2=4^2+4^2

Now you must solve for "c":

c=\sqrt{4^2+4^2}

Evaluating, you get:

c=\sqrt{16+16}\\\\c=\sqrt{32}

To simplify the result:

- Descompose 32 into its prime factors:

32=2*2*2*2*2=2^5

- By the Product of powers property, you know that:

2^5=2^4*2

- Make the substitution:

c=\sqrt{2^4*2}

- Finally, knowing that \sqrt[n]{a^n}=a, you get:

c=2^2\sqrt{2}\\\\c=4\sqrt{2}

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