Question

building a and building b are 500 meters apart. there is no road between them, so to drive from building a to building b, it is necessary to first drive to building c and then to building b. about how much farther is it to drive than to walk directly from building a to building b? round to the nearest whole number. 683 meters 183 meters 366 meters 250 meters

Explanation:

Step1: Assume a right - triangle situation

Let's assume the direct distance between building A and B is the hypotenuse of a right - triangle, and the driving path (A to C and then C to B) forms two sides of a right - triangle. But since the figure or other side lengths are not given, we assume the driving path is along two sides of a right - triangle with hypotenuse \(d_{walk}=500\) meters. Let the two sides of the right - triangle for the driving path be \(a\) and \(b\). According to the Pythagorean theorem, for a right - triangle with hypotenuse \(c\), \(a + b>c\). If we assume the driving path forms a right - triangle and we want to find the extra distance \(d\) of driving compared to walking. Let the driving distance be \(d_{drive}\) and walking distance \(d_{walk}\).

Step2: Calculate the extra distance

We need to find \(d = d_{drive}-d_{walk}\). Since we don't have enough information to calculate the driving distance exactly from the given data, we assume the most basic right - triangle case where if the two legs of the right - triangle for the driving path are \(x\) and \(y\) and hypotenuse \(z = 500\). By the Pythagorean theorem \(x^{2}+y^{2}=z^{2}=500^{2}\). And \(d_{drive}=x + y\). A well - known property of right - triangles is that for a right - triangle with legs \(x,y\) and hypotenuse \(z\), \(x + y\approx1.414z\) (for an isosceles right - triangle, \(x=y\), then \(x=y=\frac{z}{\sqrt{2}}\) and \(x + y=\sqrt{2}z\approx1.414z\)). So \(d_{drive}\approx1.414\times500 = 707\) meters. Then \(d=d_{drive}-d_{walk}\approx707 - 500=207\) meters. The closest value to our approximation among the options is 183 meters.

Answer:

183 meters