what is the height and the width of the box?

Question

The perimeter of the front of a 10-ounce cereal box is 40 inches. The height is 4 inches more than the width. What are the width and height of the front of the box?

Answer 1

Use the formula to find perimeter: P=2w + 2h, where w represents the width and h represents the height.

You know P=40,

The problems states the the height is 4 more inches than the width, so we can set up an equation h=w+4

Using these two key information, we can substitute 40 for p and w+4 for h in the perimeter formula:

40=2w+ 2(w+4) Now solve this equation for w as follows

40 = 2w + 2w +8 (Distribute 2 and multiply)

40 = 4w + 8 (combine like terms)

32 = 4w (subtract 8 from both sides)

8 = w (divide by 4 on both sides)

So the width is 8 inches.

Now we can find the height: h = w + 4 so h = 8+4 which is 12.

Height is 12 inches.

Answer 2

The front of the cereal box is a rectangular shape, so the perimeter of a rectangle is given by the following formula:

Perimeter = 2 (l + w), where l is the length and w is the width of the rectangle respectively.

Now, let us consider that the width of the front of the cereal box is x inches. Therefore, its length(height) will be x + 4 inches(as per the information in the question).

Perimeter = 2 (l + w)

Plugging in the above values, we get

40 = 2(x + 4 + x)

20 = 2x + 4

16 = 2x

x = 16/2 = 8

Therefore, the width of the front of the cereal box is 8 inches and its length(height) is 12 inches.