Answer:
[tex] \sf 4\sqrt{2} [/tex]
Step-by-step explanation:
To solve for hypotenuse(c), we can solve this using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
Given [tex]\bold{a = 4}[/tex] and [tex]\bold{b = 4}[/tex], we can find the length of the hypotenuse (c).
Using the Pythagorean theorem:
[tex] \sf c^2 = a^2 + b^2 [/tex]
Substitute the given values:
[tex] \sf c^2 = 4^2 + 4^2 [/tex]
[tex] \sf c^2 = 16 + 16 [/tex]
[tex] \sf c^2 = 32 [/tex]
Now, to find the length of [tex]\bold{c}[/tex], we take the square root of both sides:
[tex] \sf c = \sqrt{32} [/tex]
We can simplify the square root of 32:
[tex] \sf c = \sqrt{16 \times 2} [/tex]
[tex] \sf c = \sqrt{16} \times \sqrt{2} [/tex]
[tex] \sf c = 4\sqrt{2} [/tex]
So, the exact length of the hypotenuse (missing side) is [tex]\bold{ \boxed{4\sqrt{2}} }[/tex].