Question

James starts walking down A street. When he gets to B street he heads to Sarah's house to use her PS5 since he's still on that T = 15m + 50 savings plan action. James realizes it will be faster to head home via C street. If you wanted to calculate the total distance he walks ... what type of math concepts do you need to apply?

Answer 1

As you can see in the given graph the streets form a right triangle.

You can also see that the given graph is not the measure of street C.

Since the streets form a right triangle you can use Pythagoras' Theorem to find the measure of street C, like this

`\begin{gathered} a^2+b^2=c^2 \\ (2mi)^2+(1.5mi)^2=c^2 \\ 4mi^2+2.25mi^2=c^2 \\ 6.25mi^2=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{6.25mi^2}=\sqrt[]{c^2} \\ 2.5mi=c \end{gathered}`

Finally, the perimeter is the sum of all the sides of a geometric figure and since you want to know the total distance that James walked, then you need to add the measure of the 3 streets that is, calculate the perimeter formed by the 3 streets, which will be

`\begin{gathered} A\text{ street}+B\text{ street}+C\text{ street }=\text{ Total distance} \\ 2mi+1.5mi+2.5mi=\text{ Total distance} \\ 6mi=\text{ Total distance} \end{gathered}`

Then, if you want to calculate the total distance that James walks you need to apply the mathematical concepts Pythagorean Theorem and perimeter.

Therefore, the correct answer is B. Pythagorean Theorem and perimeter.