Answer:
5 cm
Step-by-step explanation:
Pythagoras theorem gives us:
[tex]hypotenuse^{2} = side^{2} + side^{2}[/tex]
We know the hypotenuse is 13 cm.
We know one side is 12 cm.
[tex]13^{2} = 12^{2} + side^{2}[/tex]
[tex]169= 144 + side^{2}[/tex]
Subtracting 144 from both sides:
[tex]25 = side^{2}[/tex]
Reversing the sides:
[tex]side^{2}=25[/tex]
[tex]\sqrt{side^{2}}= \±\sqrt{25}[/tex]
[tex]side = \±\sqrt{25}[/tex]
[tex]side = \±5[/tex]
Since a distance can't be negative:
[tex]side=5[/tex]
The third side is 5 cm.
