Answer:
Walking distance that is saved by cutting their property instead of walking around the lot is nearly 1.5 feet or
[tex]6\sqrt{21}-26\ feet[/tex]
Step-by-step explanation:
Let
Width of the lot = x feet
Length of the lot = x + 14 feet
Diagonal = 26 feet
By the Pythagorean theorem,
[tex]x^2+(x+14)^2=26^2\\ \\x^2+x^2+28x+196=676\\ \\2x^2+28x-480=0\\ \\x^2+14x-140=0\\ \\D=14^2-4\cdot 1\cdot (-140)=196+560=756\\ \\x_{1,2}=\dfrac{-14\pm\sqrt{756}}{2\cdot 1}=\dfrac{-14\pm 6\sqrt{21}}{2}=-7\pm3\sqrt{21}[/tex]
The distance cannot be negative, so
[tex]x=-7+3\sqrt{21}\\ \\x+14=-7+3\sqrt{21}+14=7+3\sqrt{21}[/tex]
Find the sum of the length and the width:
[tex]x+x+14=-7+3\sqrt{21}+7+3\sqrt{21}=6\sqrt{21}\approx 27.5\ feet[/tex]
So, walking distance that is saved by cutting their property instead of walking around the lot is nearly 1.5 feet or
[tex]6\sqrt{21}-26\ feet[/tex]
