Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.
I've added the image of the ticket as an attachment.
(a) The missing side length
From the attachment, the 4 unknown side lengths are equal. Represent this side length with L.
So, we have:
[tex]Perimeter =2\times 11 + 4 \times L[/tex]
This gives
[tex]2\times11 + 4 \times L = 42[/tex]
[tex]22 + 4 \times L = 42[/tex]
Collect like terms
[tex]4 \times L = 42-22[/tex]
[tex]4 \times L = 20[/tex]
Divide both sides by 4
[tex]L =5cm[/tex]
(b) The length of the gold lines
There are 4 slant lines and the length of one of the slant lines is 5 cm (as calculated above).
So, the length of the gold line is:
[tex]Gold = 4 \times L[/tex]
[tex]Gold = 4 \times 5cm[/tex]
[tex]Gold = 20cm[/tex]
(c) The number of gold ink bottles.
[tex]n = 200[/tex] --- number of tickets
The length of all gold line in the 200 tickets is:
[tex]Length = 200 \times Gold[/tex]
[tex]Length = 200 \times 20cm[/tex]
[tex]Length = 4000 cm[/tex]
[tex]Length = 4000 \times 0.01m[/tex] ---- convert to meters
[tex]Length = 40m[/tex]
Given that:
[tex]Bottle = 20m[/tex] --- 1 bottle for 20 m
The number of bottles (n) is:
[tex]n = \frac{Length}{Bottles}[/tex]
[tex]n = \frac{40m}{20m}[/tex]
[tex]n = 2[/tex]
Hence, 2 bottles of gold ink are enough.
Read more about perimeters at:
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