Question

casey travels from her house directly west to the bank and then directly north from the bank to the mall. she then travels home on the road connecting the mall and her house. what is her total distance traveled?

Explanation:

Step1: Identify right - triangle sides

The two legs of the right - triangle are \(a = 8\) miles and \(b = 15\) miles.

Step2: Apply Pythagorean theorem

The length of the hypotenuse \(c\) (the return journey) is calculated by \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 8\) and \(b = 15\): \(c=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17\) miles.

Step3: Calculate total distance

The other two sides of the journey are 8 miles and 15 miles. The total distance \(d=8 + 15+17\). \(d = 40\) miles.

Answer:

40 miles