Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard unto a close rectangular box. The four sides of the box have the same area, and the two ends have the same area. The area of each of the four equal sides is twice the area of each end. What is the area of each face of bills box?

Question

Alejandra Wu

Mathematics

23 April, 18:08

Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard unto a close rectangular box. The four sides of the box have the same area, and the two ends have the same area. The area of each of the four equal sides is twice the area of each end. What is the area of each face of bills box?

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Answers (1)

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Jaiden Gray · Answer 1

Step-by-step explanation:

The area of the cardboard that was used to make the box is 10 square feet.

The total surface area of the box is expressed as

2LW + 2LH + 2WH

Where

L represents the length of the box.

W represents the width of the box.

H represents the height of the box.

LW, LH and WH are the areas of the faces of the box

The four sides of the box have the same area. This means that

LW = LH

The area of each of the four equal sides is twice the area of each end. This means that

LW = LH = 2WH

Therefore, the total surface area would be

2 (2WH) + 2 (2WH) + 2WH = 10

4WH + 4WH + 2WH = 10

10WH = 10

WH = 10/10 = 1 feet

LH = 2 * 1 = 2 feet

LW = 2 * 1 = 2 feet