Question

dada a figura mostrada abaixo, determine o comprimento de c. show your work here hint: to add the square root symbol (√), type
oo

Explanation:

Step1: Find side - lengths of squares

The area of a square is $A = s^{2}$. For the square with area $A_1=64\ in^{2}$, we solve $s_1^{2}=64$ for $s_1$. So, $s_1=\sqrt{64}=8$ in. For the square with area $A_2 = 16\ in^{2}$, we solve $s_2^{2}=16$ for $s_2$. So, $s_2=\sqrt{16}=4$ in.

Step2: Apply Pythagorean theorem

The right - triangle formed by the sides of the squares has legs of lengths $a = 4$ in and $b = 8$ in. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Substituting $a = 4$ and $b = 8$ into the formula, we get $4^{2}+8^{2}=c^{2}$. Then $16 + 64=c^{2}$, so $c^{2}=80$.

Step3: Solve for $c$

Taking the square root of both sides of $c^{2}=80$, we have $c=\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}$ in.

Answer:

$4\sqrt{5}$ in