Question

c =?
a = 4
b = 6

Explanation:

Step1: Substitute values into Pythagorean theorem

Given the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, substitute $a = 4$ and $b = 6$. So we have $4^{2}+6^{2}=c^{2}$.

Step2: Calculate the left - hand side

$4^{2}=16$ and $6^{2}=36$, then $4^{2}+6^{2}=16 + 36=52$. So $c^{2}=52$.

Step3: Solve for c

Take the square root of both sides. Since $c$ represents the length of a side of a triangle, we consider the positive square root. $c=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$