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? 37 miles 17 miles 32 miles 40 miles

Explanation:

Step1: Identify the triangle sides

From the diagram, the westward (horizontal) distance (house to bank) is 8 miles, the northward (vertical) distance (bank to mall) is 15 miles. The hypotenuse (mall to house) can be found using the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 8 \), \( b = 15 \).
\( c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \) miles.

Step2: Calculate total distance

Total distance is the sum of the three sides: \( 8 + 15 + 17 \).
\( 8 + 15 = 23 \), \( 23 + 17 = 40 \) miles.

Answer:

40 miles