Question

jules owns a square plot of land that measures 30 yards on each side. he plans to divide the land in half by building a fence, as shown by the dotted line below. how many yards of fencing will jules need?
○ 15 yd
○ 30 yd
○ ( 30sqrt{2} ) yd
○ ( 30sqrt{3} ) yd

Explanation:

Step1: Identify the triangle type

The plot is a square, so triangle \(BCD\) is a right - triangle with legs \(BC = 30\) yd and \(CD=30\) yd, and the fence is the hypotenuse \(BD\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 30\), \(b = 30\), so \(BD=\sqrt{30^{2}+30^{2}}=\sqrt{900 + 900}=\sqrt{1800}=\sqrt{900\times2}=30\sqrt{2}\) yd.

Answer:

\(30\sqrt{2}\) yd (corresponding to the option \(30\sqrt{2}\) yd)