Question

Max's house has two steps on
the front porch as shown. If each
step is the same size, what is the
total vertical distance covered by
the two steps

Answer 1

Given:

Max's house has two steps on  the front porch.

Size of each step is the same.

To find:

The total vertical distance covered by  the two steps.

Solution:

From the given figure, it is clear that,

Base length of each step = 6 in

Hypotenuse = 10 in

Let h be the vertical height of each step.

Using Pythagoras theorem, the vertical height of one step is

$Base^2+Perpendicular^2=Hypotheuse^2$

$6^2+h^2=10^2$

$36+h^2=100$

$h^2=100-36$

$h^2=64$

Taking square root on both sides.

$h=\pm\sqrt{64}$

$h=\pm 8$

Height cannot be negative. So, h = 8 in.

Now,

Vertical height of 2 steps = $2\times 8$

                                         = $16$

So, the total vertical distance covered by  the two steps is 16 in.

Therefore, the correct option is A.