If a carpenter wants to make sure that a building is square and measures 768 ft and 1,024 ft along the walls, how long should he make the diagonal?
A) $1,793$ ft
B) $1,493$ ft
C) $1,567$ ft
D) $1,280$ ft
E) $1,792$ ft

Question

Quizplus · Accepted Answer

To find the length of the diagonal in a right-angled triangle (which is the case here, assuming the building is square in layout), we use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the two sides, and $c$ is the length of the diagonal. Plugging in the given lengths, $768^2 + 1024^2 = c^2$, which simplifies to $589,824 + 1,048,576 = c^2$, and further to $1,638,400 = c^2$. Taking the square root of both sides gives $c = 1,280$ ft.

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