We are given that Caleb followed two paths to get to his house C from a store S, and we're asked to evaluate the total distance of the two paths. Let's take a look at a diagram describing this situation. Let x and y be the distances of Path 1 and Path 2.
First, we can solve for y. Notice that this segment is a hypotenuse of a right triangle.
To find the value of y we can use the Pythagorean Theorem. According to this theorem, the sum of the squared legs is equal to its squared hypotenuse. Let's write an equation using this theorem.
10^2+ 4^2= y^2
Now we will solve the above equation. Notice that since y represents the distance, we will consider only the positive case when taking a square root of y^2.
The distance of Path 2 is approximately 10.8 meters. Let's add this information to our diagram.
Next, we will find the value of x. First, we should evaluate the legs of the right triangle that has a hypotenuse of x. We can call them a and b.
To do this, we will evaluate the appropriate differences of segments.
a= 15-10=5
b=28- 4=24
Let's add this information to our diagram.
Now we will find the value of x by using the Pythagorean Theorem again. Let's write an equation.
5^2+24^2= x^2
Next we will solve the above equation. Notice that since x represents the distance, we will consider only the positive case when taking a square root of x^2.
The distance of Path 1 is approximately 24.5 meters. Finally, we will add the distances of both paths to find the total distance.
24.5+ 10.8=35.3
The toal distance of the two paths is approximately 35.3 meters. This corresponds with answer D.
