contestada

A straw is placed inside a rectangular box that is 6 inches by 2 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Respuesta :

retirEEd

Answer:

Step-by-step explanation:

Use the Pythagorean theorem twice once to find the diagonal 1 along the bottom of the box  and the to find the diagonal 2 using diagonal 1 and the height of the box  

l² + w² = d1²

d1² + h² = d2²

(l² + w²) + h² = d2²

6² + 2² + 4² = d2²

48 = d2²

d2 = √48

d2 = √(16)(3)

d2 = 4√3

MrRoyal

The length of the straw is [tex]2\sqrt{14[/tex] inches

The given parameters are:

  • Length (l) = 6 inches
  • Width (w) = 2 inches
  • Height (h) = 4 inches

The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

[tex]s = \sqrt{l^2 + w^2 + h^2[/tex]

The equation becomes

[tex]s = \sqrt{6^2 + 2^2 + 4^2[/tex]

Evaluate the exponents

[tex]s = \sqrt{56[/tex]

Express 56 as 4 * 16

[tex]s = \sqrt{4 \times 14[/tex]

Evaluate the square root of 4

[tex]s = 2\sqrt{14[/tex]

Hence, the length of the straw is [tex]2\sqrt{14[/tex]

Read more about rectangular box at:

https://brainly.com/question/2291999

Otras preguntas