A diagonal shortcut across an empty rectangular lot is 97 feet. The lot is 72 feet long. What is the other dimension of the lot? Round your answer to the nearest tenth.

To find the width of a rectangular lot with a diagonal of 97 feet and a length of 72 feet, apply the Pythagorean theorem. By subtracting the square of the length from the square of the diagonal and taking the square root, you find that the width is approximately 65 feet.

Explanation:

The student asked for the width of a rectangular lot, given that the diagonal is 97 feet and the length is 72 feet. This problem can be solved using the Pythagorean theorem which is a fundamental principle in geometry for right-angled triangles.

According to the Pythagorean theorem, the square of the length of the diagonal (hypotenuse) equals the sum of the squares of the other two sides (length and width). The formula is c2 = a2 + b2, where c represents the diagonal, and a and b represent the length and width, respectively.

Step-by-step solution:

Let the width be w.
Plug the given values into the Pythagorean theorem: 972 = 722 + w2.
Solve for w: 972 - 722 = w2.
Calculate the left side of the equation: 9409 - 5184 = w2 which simplifies to 4225 = w2.
Find the square root of 4225 to find w: w = 65.

Therefore, the other dimension of the lot, the width, is approximately 65 feet.