Question

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

Explanation:

Step1: Find side - lengths of known squares

The area of a square is $A = s^{2}$, where $s$ is the side - length. For the square with area $16\ in^{2}$, we have $s_1^{2}=16$, so $s_1 = 4$ inches (since $s>0$). For the square with area $52\ in^{2}$, if its side - length is $s_2$, then $s_2^{2}=52$.

Step2: Apply the Pythagorean theorem

In the right - triangle formed by the sides of the squares, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a$ is the side of the $16\ in^{2}$ square, $b$ is the unknown side, and $c$ is the side of the $52\ in^{2}$ square. Let $a = 4$ and $c^{2}=52$. Then $4^{2}+b^{2}=52$.

Step3: Solve for $b$

We have $16 + b^{2}=52$. Subtract 16 from both sides: $b^{2}=52 - 16=36$. Taking the square root of both sides (and considering the positive value since length is non - negative), $b = 6$ inches.

Answer:

6 inches