Question

dada a figura mostrada abaixo, determine o comprimento de b. show your work here hint: to add the square root symbol (√), type
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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 $A_1 + A_2=A_3$. Here, if the side - length of the square with area $16\ in^2$ is $a$, $a^2 = 16$, and if the side - length of the square with area $65\ in^2$ is $c$, $c^2 = 65$, and the side - length of the square with side $b$ is $b$ itself, so $b^{2}+16 = 65$.

Step2: Solve for $b^{2}$

Subtract 16 from both sides of the equation $b^{2}+16 = 65$. We get $b^{2}=65 - 16$.
$b^{2}=49$

Step3: Solve for $b$

Take the square root of both sides. Since $b$ represents a length, we consider the positive square root. $b=\sqrt{49}$.
$b = 7$

Answer:

$7$ in