SOLUTION: The longest drive to the center of a square city from the outskirts is 10 miles. Within the last decade the city has expanded in area by 50 sq mi. Assuming the city has always been

Question 514242: The longest drive to the center of a square city from the outskirts is 10 miles. Within the last decade the city has expanded in area by 50 sq mi. Assuming the city has always been square in shape, find the corresponding change in the longest drive to the center of the city.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The longest drive to the center of a square city from the outskirts is 10 miles. Within the last decade the city has expanded in area by 50 sq mi. Assuming the city has always been square in shape, find the corresponding change in the longest drive to the center of the city.
**
Longest drive to the center of a square city is half the distance of the diagonals.
let x=length of one side of the square.
At present:
Diagonol=20 mi
by Pythagorean Theorem
x^2+x^2=20^2=400
2x^2=400
x^2=200
area=200 sq mi
..
10 years ago:
area=200-50=150 sq mi
x^2=150
2x^2=300
diagonal=√300=17.32 mi
longest drive to center of city=17.32/2=8.66 mi
..
change in the longest drive to the center of the city compared to decade ago=10-8.66=1.34 mi increase
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