Answered

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A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 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.

Sagot :

MrRoyal

Answer:

[tex]2\sqrt{42}[/tex]

Step-by-step explanation:

Given

[tex]l = 10in[/tex] --- Length

[tex]w = 8in[/tex] --- Width

[tex]h = 2in[/tex] --- Height

Required: Determine the length of the straw

Since the straw fits the diagonal of the box, the length of the straw is equivalent of the length of the diagonal.

The length of the diagonal is calculated as:

[tex]\displaystyle d = \sqrt{w^{2} + l^{2} + h^{2}}[/tex]

[tex]\displaystyle d = \sqrt{8^{2} + 10^{2} + 2^{2}}[/tex]

[tex]\displaystyle d = \sqrt{64 + 100 + 4}[/tex]

[tex]\displaystyle d = \sqrt{168}[/tex]

[tex]\displaystyle d = \sqrt{4*42}[/tex]

Split

[tex]\displaystyle d = \sqrt{4}*\sqrt{42}[/tex]

[tex]\displaystyle d = 2*\sqrt{42}[/tex]

[tex]\displaystyle d = 2\sqrt{42}[/tex]

Hence, the straw length is: [tex]2\sqrt{42}[/tex]

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