17) A spider has taken up residence in a small cardboard box which measures 8 inches by 5 inches by 4 inches.
The spider travels from the lower right front corner of
the box to the upper left back corner of the box.
What is the length, in inches, that the spider travels?
Show your work and use mathematical vocabulary
to explain your reasoning.
4
8

10.2 in.

Step-by-step explanation:

You need to use the Pythagorean theorem twice.

First, draw a diagonal of the base of the box going from the front right side to the back left side.

That diagonal is the hypotenuse of a right triangle with legs measuring 8 in. and 5 in.

For this right triangle, I will use a and b for the legs and c for the hypotenuse.

c^2 = a^2 + b^2

c^2 = (8 in.)^2 + (5 in.)^2

c^2 = 89 in.^2

Now use the diagonal and the back left edge of the box as legs, and the path of the spider as a hypotenuse in a new right triangle.

For this right triangle, I will use A and B for the legs, and C for the hypotenuse. Notice that leg A of this case is hypotenuse c of the previous right triangle.

C^2 = A^2 + B^2

C^2 = 89 in.^2 + (4 in.)^2

C^2 = 105 in^2

C = 10.2 in.

The length is 10.2 in.