The Great Pyramid of Giza is the oldest and largest of the pyramids in Egypt. It is believed the pyramid was built as a tomb for the Pharaoh Khufu. The completed design dimensions are estimated to have originally been 280 cubits in height by 440 cubits in length for each of the four sides of its square base. The base of a square pyramid is laid out so that each of the four sides measures 440 cubits.

What must the measure of both diagonals be, in cubits, to insure that the base is a square? Round your answer to the nearest hundredth.

Question

The Great Pyramid of Giza is the oldest and largest of the pyramids in Egypt. It is believed the pyramid was built as a tomb for the Pharaoh Khufu. The completed design dimensions are estimated to have originally been 280 cubits in height by 440 cubits in length for each of the four sides of its square base. The base of a square pyramid is laid out so that each of the four sides measures 440 cubits.

What must the measure of both diagonals be, in cubits, to insure that the base is a square? Round your answer to the nearest hundredth.

anonymous · Answer

A. 	The diagonals of a square are the same length. The Pythagorean Theorem can be used to find the diagonal of this square, since the length of the sides of the square are known.

a2 + b2 = c2
(440)2 + (440)2 = c2
193,600 + 193,000 = c2
387,000 = c2
622.25 = c


	B. 	The diagonals of a square are the same length. The Pythagorean Theorem can be used to find the diagonal of a square if the side of the square is known.

a + b = c
440 + 440 = c
880 = c

The length of each diagonal of the square base is 880 cubits.