6. chris is mailing his friend a poster that has been rolled up in a long tube. he has a box that measures…
6. chris is mailing his friend a poster that has been rolled up in a long tube. he has a box that measures 20 inches by 8 inches by 4 inches. what is the maximum length the rolled poster can be?
Answer
Explanation:
Step1: Encontrar la diagonal de la base
La base del cubo tiene dimensiones (8) pulgadas y (4) pulgadas. Usando el teorema de Pitágoras (d_{base}=\sqrt{8^{2}+4^{2}}). [ \begin{align*} d_{base}&=\sqrt{64 + 16}\ &=\sqrt{80}\ &=4\sqrt{5}\text{ pulgadas} \end{align*} ]
Step2: Encontrar la diagonal del cubo
La altura del cubo es (20) pulgadas. Usando el teorema de Pitágoras con la diagonal de la base (d_{base}) y la altura (h = 20) para encontrar la diagonal del cubo (d). [ \begin{align*} d&=\sqrt{(4\sqrt{5})^{2}+20^{2}}\ &=\sqrt{80+400}\ &=\sqrt{480}\ &=\sqrt{16\times30}\ & = 4\sqrt{30}\approx4\times5.477\ &=21.908\approx21.91\text{ pulgadas} \end{align*} ]
Answer:
La longitud máxima del póster enrollado es aproximadamente (21.91) pulgadas.