Answer:
17 feet
Step-by-step explanation:
Length of the diagonal=50 feet
Let the shorter part of the sidewalk =x
Since the longer part of the sidewalk is twice the shorter length,
Length of the longer part of the sidewalk =2x
First, we determine the value of x.
Using Pythagoras Theorem and noting that the diagonal is the hypotenuse.
[tex]50^2=(2x)^2+x^2\\5x^2=2500\\$Divide both sides by 5\\x^2=500\\x=\sqrt{500}=10\sqrt{5} \:ft[/tex]
The length of the shorter side =[tex]10\sqrt{5} \:ft[/tex]
The length of the longer side =[tex]20\sqrt{5} \:ft[/tex]
Total Distance =[tex]10\sqrt{5}+ 20\sqrt{5}=67 \:feet[/tex]
Difference in Distance
67-50=17 feet
The children are saving 17 feet by cutting the lawn diagonally.
