Question

working with the pythagorean theorem: part 2
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youre looking at a new laptop that has a diagonal length of 15 inches. you already have a laptop cover that has a width of 8 inches and a length of 12 inches. will the new laptop fit in your old laptop cover? why or why not?
no, the new laptop will not fit, because the cover has a diagonal length between 8 and 9 inches, which is smaller than the new laptop.
no, the new laptop will not fit, because the cover has a diagonal length between 14 and 15 inches, which is smaller than the new laptop.
yes, the new laptop will fit because the cover has a diagonal length of 15 inches.

Explanation:

Step1: Calculate cover's diagonal

Use Pythagorean theorem: $d = \sqrt{8^2 + 12^2}$
$d = \sqrt{64 + 144} = \sqrt{208}$

Step2: Approximate diagonal value

$\sqrt{196}=14$, $\sqrt{225}=15$, so $\sqrt{208}\approx14.42$ (between 14 and 15)

Step3: Compare with laptop's diagonal

New laptop's diagonal is 15 inches, which is larger than ~14.42 inches.

Answer:

No, the new laptop will not fit, because the cover has a diagonal length between 14 and 15 inches, which is smaller than the new laptop.