Question

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Answer 1

12 cm

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) } = √(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!!