Question

math problem ben and jerry live on a corner lot. often neighborhood children cut across their lot to save walking distance. if the length of their lot is 14 feet more than its width and the path across their lot is 26 feet, how many feet of walking distance is saved by cutting their property instead of walking around the lot

Answer 1

Walking distance that is saved by cutting their property instead of walking around the lot is nearly 1.5 feet or

`6√(21)-26\ feet`

Explanation:

Let

Width of the lot = x feet

Length of the lot = x + 14 feet

Diagonal = 26 feet

By the Pythagorean theorem,

`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)=(-14\pm√(756))/(2\cdot 1)=(-14\pm 6√(21))/(2)=-7\pm3√(21)`

The distance cannot be negative, so

`x=-7+3√(21)\\ \\x+14=-7+3√(21)+14=7+3√(21)`

Find the sum of the length and the width:

`x+x+14=-7+3√(21)+7+3√(21)=6√(21)\approx 27.5\ feet`

So, walking distance that is saved by cutting their property instead of walking around the lot is nearly 1.5 feet or

`6√(21)-26\ feet`