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

20 kilometers

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.

`√(400)=√(h^2)`

`√(400)=h`

`20=h`

h= 20 km

The value of h is 20 kilometers.

Answer 2

h = 20 km

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