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What is the longest diagonal of a rectangular box that is $120 inches$ long, $90 inches wide$ , and $80 inches$ tall?

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170

120

150

190

answer is A.

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Detailed Solution

Here, we will be using the “Deluxe Pythagorean Theorem”, to find the value of the longest diagonal present in the rectangular box.
The “Deluxe Pythagorean Theorem” says that if there are three sides given,

a, b and c

of a rectangle given, then according to the theorem,

a^{2} + b^{2} + c^{2} = d^{2}

.
Now, according to the question,

a = 120 inches

b = 90 inches

c = 80 inches

Therefore,

a^{2} + b^{2} + c^{2} = d^{2}

\Rightarrow {(120)}^{2} + {(90)}^{2} + {(80)}^{2} = d^{2}

\Rightarrow 14400 + 8100 + 6400 = d^{2}

\Rightarrow d^{2} = 28900

\Rightarrow d = \sqrt{28900}

\Rightarrow d = 170

Therefore, the longest diagonal of the rectangular box is:

170 inches

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