So quick recap: a ratio is used to show a comparison between two different things.
If you are given a ratio of 1:5, this means that the second quantity is five times as large as the first.
Part A: Asks you to find the area of the original painting. Since the ratio of the postcard painting to the original painting is 1:5, the original painting is five times larger than the postcard, or (4 x 5) by (6 x 5) inches, or 20 by 30 inches.
Part B: There is some deleted text that cannot give me information on how tall the tree is. (Maybe you were voice recording?)
I hope I at least answered Part A. Good luck :)
Answer:
A) 600 square inches
B) 8 inches
Step-by-step explanation:
To find the area, in square inches, of the original painting, we need to use the scale factor given.
The dimensions of the postcard are 4 in × 6 in, and the scale factor of the postcard painting to the original painting is represented by the ratio 1 : 5. This means that 1 inch in the postcard painting represents 5 inches in the original painting.
First, find the dimensions of the original painting by multiplying the dimensions of the postcard by 5:
[tex]\rm 4 \times 5 = 20\; inches\\\\6 \times 5 = 30\; inches[/tex]
Now, multiply the new dimensions by each other to find the area of the original painting:
[tex]\rm Area\;of\;the\;original\;painting=20 \times 30\\\\Area\;of\;the\;original\;painting=600\; square\;inches[/tex]
Therefore, the area of the original painting is:
[tex]\Large\boxed{\boxed{600\; \rm square\;inches}}[/tex]
[tex]\dotfill[/tex]
Since the scale factor is 1 : 5, this means that any length in the original painting is 5 times larger than in the postcard painting.
If the tree in the postcard painting has a height of 1.6 inches, then in the original painting, its height would be 5 times this:
[tex]\rm Height\;of\;tree= 1.6 \times 5\\\\Height\;of\;tree= 8\; inches[/tex]
Therefore, the height of the tree in the original painting is:
[tex]\Large\boxed{\boxed{ \rm 8\; inches}}[/tex]
