Question

start by substituting the value of a and b in the pythagorean theorem equation. the pythagorean theorem says that if a, b, and c are the sides of a right triangle, where c is the hypotenuse, then: $a^{2}+b^{2}=c^{2}$. $c =?$ $a = 4$ $a^{2}+b^{2}=c^{2}$ $b = 6$ $□^{2}+□^{2}=c^{2}$

Explanation:

Step1: Substitute values

Substitute $a = 4$ and $b = 6$ into $a^{2}+b^{2}=c^{2}$. So we get $4^{2}+6^{2}=c^{2}$.

Step2: Calculate squares

Calculate $4^{2}=16$ and $6^{2}=36$. Then the equation becomes $16 + 36=c^{2}$, i.e., $c^{2}=52$.

Step3: Find c

Take the square - root of both sides. Since $c>0$ (as it represents the length of a side of a triangle), $c=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$c = 2\sqrt{13}$