The combined volume of the three boxes is 1,197 cubic inches. • The area of one face of the medium box is 49 square inches. • The volume of the smallest box is 218 cubic inches less than the volume of the medium box. 1. What is the volume of the medium box? Explain. 2. What is the area of one face of the smallest box? Explain. 3. What is the edge length of the largest box? Explain. 4. What is the total height of the stack of boxes? How do you know? 5. Paul wants to gift wrap the boxes. He has 1,000 in. 2of wrapping paper. Does Paul have enough paper to wrap all three boxes? Explain.

20

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240