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 with squares on its sides, if the areas of the squares are $A_1$, $A_2$, and $A_3$ corresponding to the sides $a$, $b$, and $c$ of the right - triangle ($c$ being the hypotenuse), then $A_1+A_2 = A_3$. Here, let the side of the square with area $64\ cm^2$ be $a$, the side of the square with area $113\ cm^2$ be $c$, and the side of the square with side length $b$ be $b$. We know that if the area of a square is $A = s^2$, then $s=\sqrt{A}$. So, $a^2 = 64$ and $c^2=113$.

Step2: Apply Pythagorean theorem formula

According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$. We can solve for $b^{2}$: $b^{2}=c^{2}-a^{2}$. Substitute $a^{2}=64$ and $c^{2}=113$ into the formula. So, $b^{2}=113 - 64$.

Step3: Calculate $b^{2}$

$b^{2}=113 - 64=49$.

Step4: Find $b$

Since $b^{2}=49$ and $b>0$ (as it represents a length), then $b=\sqrt{49}=7\ cm$.

Answer:

$7\ cm$