Answer:
20 kilometers
Step-by-step explanation:
Mario will form a right triangle. The legs of the right triangle will be 16 and 12, from the 16 kilometers west and 12 kilometers south he walked.
Since it is a right, triangle, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse.
We know that 16 and 12 are the legs. h will be the hypotenuse.
[tex]a=16\\b=12 \\c=h[/tex]
Substitute the values into the formula.
[tex]16^2+12^2=h^2[/tex]
Now we must solve for [tex]h[/tex] by isolating it. First, evaluate the exponents on the left side.
⇒ 16²=16*16=256
[tex]256+12^2=h^2[/tex]
⇒12²=12*12=144
[tex]256+144=h^2[/tex]
Add 256 and 144.
[tex]400=h^2[/tex]
[tex]h[/tex] is being squared. The inverse of a square is the square root. Take the square root of both sides of the equation.
[tex]\sqrt{400}=\sqrt{h^2}[/tex]
[tex]\sqrt{400}=h[/tex]
[tex]20=h[/tex]
h= 20 km
The value of h is 20 kilometers.
