Answer:
12 cm
Step-by-step explanation:
The Pythagorean Theorem is as follows:
[tex]a^{2} +b^{2} =c^{2}[/tex]
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:
[tex]a^{2} + (5^{2}) = (13^{2})[/tex]
Solve for the other leg:
[tex]a^{2} + 25 = 169[/tex] Square what's in the parentheses from above
[tex]a^{2} = 144\\[/tex] Subtract 25 from 169
[tex]\sqrt{a^{2} } = \sqrt{144}[/tex] Square root both sides
a = 12 cm
Thus, the length of the other leg is 12 cm.
Let's check our answer:
[tex]12^{2} +5^{2} =13^{2}[/tex] 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!!
