Answer :
To solve for the other dimension of the lot, which we will call the width, we can use the Pythagorean Theorem. The Pythagorean Theorem is used to relate the lengths of the sides of a right-angled triangle. Since the diagonal of a rectangle divides it into two right-angled triangles, we can use this theorem to solve for the missing side.
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is:
\[ c^2 = a^2 + b^2 \]
In the context of the rectangular lot, the hypotenuse will be the diagonal (97 feet), one side will be the length of the lot (72 feet), and the other side we're trying to find is the width (we will call it 'w'). So, we can set up the equation as:
\[ 97^2 = 72^2 + w^2 \]
Let's solve for the width by first calculating the squares of the diagonal and the length:
\[ 97^2 = 9409 \]
\[ 72^2 = 5184 \]
Subtracting the square of the length from the square of the diagonal gives us:
\[ w^2 = 9409 - 5184 \]
\[ w^2 = 4225 \]
To find the width 'w', we take the square root of the width squared:
\[ w = \sqrt{4225} \]
\[ w = 65 \]
Therefore, the other dimension of the lot, the width, is 65 feet.
