Question

a rectangular garden is 3 feet wide. if the garden is 11 feet from corner to corner, as shown in the figure, how long is the garden? 3 ft 11 ft

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the garden be \( l \). According to the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( a = 3\) (width), \( c=11\) (diagonal), and \( b = l\) (length). So \( 3^{2}+l^{2}=11^{2} \).

Step2: Simplify the equation

\( 9 + l^{2}=121 \). Then \( l^{2}=121 - 9\).

Step3: Calculate \( l^{2}\)

\( l^{2}=112 \).

Step4: Solve for \( l\)

\( l=\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\approx 10.6 \)

Answer:

The length of the garden is approximately \( 10.6\) feet.