Question

Paul bicycles 12 kilometers west to get from his house to school. After school, he bicycles 9 kilometers north to his friend Roger's house. How far is Paul's house from Roger's house, measured in a straight line?

Option 1: 15 kilometers
Option 2: 21 kilometers
Option 3: 27 kilometers
Option 4: 15.6 kilometers

Answer 1

To find the distance between Paul's house and Roger's house, we can use the Pythagorean theorem. The distance is 15 kilometers.

Step-by-step explanation:

To find the distance between Paul's house and Roger's house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, Paul's westward distance of 12 kilometers and northward distance of 9 kilometers form the legs of a right triangle. Therefore, the distance between his house and Roger's house can be found using the formula:

Distance = √((12km)^2 + (9km)^2) = √(144km^2 + 81km^2) = √225km^2 = 15km

So, the distance between Paul's house and Roger's house, measured in a straight line, is 15 kilometers.