Question

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Answer 1

Answer:

12 cm

Step-by-step explanation:

The Pythagorean Theorem is as follows:

$a^{2} +b^{2} =c^{2}$

A and B represent the side lengths (legs) and C represents the hypotenuse.

The length of one leg equals 5cm. (This can be represented by either a or b)

The hypotenuse equals 13 cm.

Plug these into the equation from above:

$a^{2} + (5^{2}) = (13^{2})$

Solve for the other leg:

   $a^{2} + 25 = 169$                          Square what's in the parentheses from above

$a^{2} = 144$                                  Subtract 25 from 169

$\sqrt{a^{2} } = \sqrt{144}$                            Square root both sides

a = 12 cm                        

Thus, the length of the other leg is 12 cm.

Let's check our answer:

$12^{2} +5^{2} =13^{2}$                        Square everything

144 + 25 = 169                      Add

169 = 169

Because both sides are equal it means that 12 cm is the correct answer.

Hope this helps!!