Jimmy ran 3 miles west from home and then turned north and jogged 4 miles. In a straight line, how far is Jimmy from home?
A 3.5 miles
B 4 miles
C 5 miles
D 7 miles
E 17 miles
Jimmy’s Jogging Distance from Home
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The correct answer is C: 5 miles.
To find out how far Jimmy is from home in a straight line, we can use the Pythagorean theorem. He first ran 3 miles west and then 4 miles north. These two distances form a right triangle, where:
– One leg of the triangle is 3 miles (west).
– The other leg of the triangle is 4 miles (north).
According to the Pythagorean theorem:
( c^2 = a^2 + b^2 )
Where:
– ( c ) is the hypotenuse (the distance from home),
– ( a ) is one leg (3 miles),
– ( b ) is the other leg (4 miles).
Now, substituting the values:
( c^2 = 3^2 + 4^2 )
( c^2 = 9 + 16 )
( c^2 = 25 )
( c = sqrt{25} )
( c = 5 )
So, Jimmy is 5 miles away from home.