Answer:
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.
Answer: The length is 10.2 in.
