Question

Mario’s car has run out of gasoline. He walks 16 km west and then 12 km south looking for a gasoline station. If he is now h km directly from his starting point, find the value of h

Answer 1

Answer:

h = 20 km

Step-by-step explanation:

Mario's path forms a right triangle with legs 16 km and 12 km and hypotenuse h. Let's use the Pythagorean Theorem (a² + b² = c²) to solve for h.

16² + 12² = h²

256 + 144 = h²

400 = h²

h = 20 km

Answer 2

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.

$a^2+b^2=c^2$

where $a$ and $b$ are the legs and $c$ is the hypotenuse.

We know that 16 and 12 are the legs. h will be the hypotenuse.

$a=16\\b=12 \\c=h$

Substitute the values into the formula.

$16^2+12^2=h^2$

Now we must solve for $h$ by isolating it. First, evaluate the exponents on the left side.

⇒ 16²=16*16=256

$256+12^2=h^2$

⇒12²=12*12=144

$256+144=h^2$

Add 256 and 144.

$400=h^2$

$h$ is being squared. The inverse of a square is the square root. Take the square root of both sides of the equation.

$\sqrt{400}=\sqrt{h^2}$

$\sqrt{400}=h$

$20=h$

h= 20 km

The value of h is 20 kilometers.