Question

dada a figura mostrada abaixo, determine o comprimento de b.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, if the areas of the squares on the two legs and the hypotenuse are $A_1$, $A_2$, and $A_3$ respectively, then $A_1 + A_2=A_3$. Let the area of the square with side - length $b$ be $A_1$, the area of the other leg's square be $A_2 = 25$ in², and the area of the hypotenuse's square be $A_3 = 41$ in². So, $A_1+25 = 41$.

Step2: Solve for the area of the square with side - length $b$

$A_1=41 - 25$.
$A_1 = 16$ in².

Step3: Find the side - length $b$

Since the area of a square $A = b^2$ and $A = 16$ in², then $b=\sqrt{16}$.
$b = 4$ in.

Answer:

$4$ in