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zlopas [31]
3 years ago
9

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

Mathematics
1 answer:
scoundrel [369]3 years ago
8 0

Answer:

2\sqrt{42}

Step-by-step explanation:

Given

l = 10in --- Length

w = 8in --- Width

h = 2in --- Height

Required: Determine the length of the straw

<em>Since the straw fits the diagonal of the box, the length of the straw is equivalent of the length of the diagonal.</em>

The length of the diagonal is calculated as:

\displaystyle d = \sqrt{w^{2} + l^{2} + h^{2}}

\displaystyle d = \sqrt{8^{2} + 10^{2} + 2^{2}}

\displaystyle d = \sqrt{64 + 100 + 4}

\displaystyle d = \sqrt{168}

\displaystyle d = \sqrt{4*42}

Split

\displaystyle d = \sqrt{4}*\sqrt{42}

\displaystyle d = 2*\sqrt{42}

\displaystyle d = 2\sqrt{42}

Hence, the straw length is: 2\sqrt{42}

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