Question

a college plans a new walkway through a rectangular patio, as shown. dimensions are in yards (yd). what will be the length, in yards, of the new walkway? round your answer to the nearest yard.

Explanation:

Step1: Identify the right - angled triangle

The walkway forms the hypotenuse of a right - angled triangle with legs of lengths 8 yd and 12 yd.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 8\), \(b = 12\), and \(c\) is the length of the hypotenuse (the walkway). So \(c=\sqrt{8^{2}+12^{2}}=\sqrt{64 + 144}=\sqrt{208}\).

Step3: Calculate and round

\(\sqrt{208}\approx14.42\). Rounding to the nearest yard, we get 14 yd.

Answer:

14 yd