The perimeter of a shape is the sum of the visible lengths of the shape. Adam does not have enough ribbon to decorate the top of the box.
I've added the gift box, as an attachment.
From the attached image, we have:
[tex]Volume = 296[/tex]
[tex]Height = 8[/tex]
Next, we calculate the length and the width of the box using:
[tex]Volume = Length \times Width \times Height[/tex]
The top and bottom edges are square. This means that:
[tex]Length = Width[/tex]
So, we have:
[tex]Volume = Length \times Length \times Height[/tex]
Substitute known values
[tex]296 = Length \times Length \times 8[/tex]
[tex]296 = Length^2 \times 8[/tex]
Divide both sides by 8
[tex]37 = Length^2[/tex]
Take square roots of both sides
[tex]6.1 = Length[/tex]
So, we have:
[tex]Length = Width = 6.1[/tex]
Calculate perimeter (P) of the top edge of the box
[tex]P =2 \times (Length + Width)[/tex]
[tex]P =2 \times (6.1 + 6.1)[/tex]
[tex]P =2 \times (12.2)[/tex]
[tex]P =24.4[/tex]
This means that Adam needs 24.4 cm of gold ribbon to wrap the top edge
By comparison:
[tex]24.4 > 24\frac 14[/tex]
or
[tex]24.4 > 24.25[/tex]
24.4 cm is greater than the length of Adam's gold ribbon (24.25).
Hence, we can conclude that he does not have enough ribbon to decorate the top of the box.
Learn more about perimeters at:
https://brainly.com/question/6465134
