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Whenever she visits Newport, Ashley has to drive $12$ miles due north from home. Whenever she visits Fairfax, she has to drive $16$ miles due east from home. How far apart are Newport and Fairfax, measured in a straight line? $\newline$ $\_\_\_\_$ miles

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Pythagorean theorem: word problems

Full solution

Q. Whenever she visits Newport, Ashley has to drive

12

miles due north from home. Whenever she visits Fairfax, she has to drive

16

miles due east from home. How far apart are Newport and Fairfax, measured in a straight line?

\newline

\_\_\_\_

miles

Identify Problem and Values: Step $1$ : Identify the problem and the known values. $\newline$ Ashley drives $12$ miles north to Newport and $16$ miles east to Fairfax. We need to find the straight-line distance between Newport and Fairfax. $\newline$ North and east directions form a right angle, so we can use the Pythagorean theorem.
Set up Pythagorean Theorem: Step $2$ : Set up the Pythagorean theorem. $\newline$ Let $d$ be the distance between Newport and Fairfax. $\newline$ Using the theorem: $(\text{North distance})^2 + (\text{East distance})^2 = (\text{Diagonal distance})^2$ $\newline$ $12^2 + 16^2 = d^2$
Calculate Squares of Distances: Step $3$ : Calculate the squares of the distances. $\newline$ $12^2 = 144$ $\newline$ $16^2 = 256$ $\newline$ Now, add these to find $d^2$ . $\newline$ $144 + 256 = 400$
Solve for Distance: Step $4$ : Solve for $d$ . $\newline$ To find $d$ , take the square root of $400$ . $\newline$ $\sqrt{400} = 20$ $\newline$ So, the distance between Newport and Fairfax is $20$ miles.

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