Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
This is a 45-45-90 right triangle.
The relationship between the hypotenuse and the legs is that the hypotenuse is equal to the length of the leg multiplied by
Therefore, you can represent the length of the leg as s:
10 = s[tex]\sqrt{2}[/tex]
Now, divide both sides by [tex]\frac{10}{\sqrt{2}}[/tex] to get s by itself:
s = [tex]\frac{10}{\sqrt{2}}[/tex]
Since having a radical (root) in the denominator is not technically simplified, we must "rationalize the denominator". To do so, multiply the numerator and denominator of the fraction by the radical over the radical:
[tex]\frac{10}{\sqrt{2}}[/tex] · [tex]\frac{\sqrt{2}}{\sqrt{2}}[/tex].
Now, multiply the fractions and simplify:
[tex]\frac{10\sqrt{2}}{2}[/tex]
5[tex]\sqrt{2}[/tex]
