Verified Answer :

meerkat18

The path that Dave drove and the direct road going northeast form a right triangle with legs 20 miles and 15 miles. What is asked in the problem is the hypotenuse of the triangle, x. Using the Pythagorean equation,
                                20² + 15² = x²
The equation yields a value of x equal to 25. Thus, Dave would have to drive 25 miles only.

Dave has to drive 25 miles northeast if there were a direct road.

The problem uses Pythagorean theorem wherein 20 miles east and 15 miles north are two legs of a triangle.

Using the equation: a^2+b^2=c^2

20^2+15^2= c^2
\(400+225=\sqrt{c^{2} }\)
c=25 miles

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