Question

When the ancient Egyptians were building the great pyramids at Giza, they checked each course of level of stone to make sure they were being laid square by measuring the diagonals. Each course of stones has the length of the square reduced by 2 meters. What is the reduction in the length of each diagonal?

Answer 1

To find the reduction in the length of each diagonal of the square, we can use the Pythagorean theorem and algebraic expressions.

Step-by-step explanation:

To find the reduction in the length of each diagonal, we will first calculate the length of each diagonal of a course of stones.

Let's assume the original length of each side of the square is x meters. If each course of stones has the length of the square reduced by 2 meters, then the new length of each side is (x - 2) meters.

Using the Pythagorean theorem, we can find the length of the diagonal of the square, which is equal to √2 times the length of each side.

So, the original length of the diagonal is √2x meters, and the new length is √2(x - 2) meters. The reduction in the length of each diagonal is √2x - √2(x - 2) meters.