You want to draw an enlargement of a design that is printed on a card that is 5 in. by 6 in. You will be drawing this design on an piece of paper that is mc003-1.jpg in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
No idea what "mc003-1.jpg in. by 11 in" is supposed to say, but the 11 in
suggests you might be talking about the standard US paper size of
8.5 by 11 inches.
so you want to maintain the 5 : 6 ratio of the original card.
if we change the width from 5 inches to 8.5 inches, then we have to
increase the length to (8.5/6)*6 or 10.2 inches
let see if the longest side can be stretched to fit the 11 inches
stretch factor is 11/6
will the width work?, that is, what is 11/6*5 ?
I get 9.166.. which is greater than the 8.5 that the paper will allow
so .....
the largest card I can make is 8.5 inches by 10.2 inches
note: 10.2 : 8.5 = 6:5
n
To find the dimensions of the largest complete enlargement you can make, you need to determine the scale factor between the card and the piece of paper, and then multiply the dimensions of the card by the scale factor.
First, let's find the scale factor by comparing the length of the card to the length of the paper:
Scale factor = Length of the paper / Length of the card
Scale factor = 11 in. / 6 in.
Now, let's find the scale factor by comparing the width of the card to the width of the paper:
Scale factor = Width of the paper / Width of the card
Scale factor = 11 in. / 5 in.
We will use the smaller of the two scale factors, which is the one obtained from comparing the width of the card to the width of the paper.
Scale factor = 11 in. / 5 in.
Scale factor = 2.2
Now, multiply the dimensions of the card by the scale factor to find the dimensions of the largest complete enlargement:
Length of the largest complete enlargement = Length of the card x Scale factor
Length of the largest complete enlargement = 6 in. x 2.2
Width of the largest complete enlargement = Width of the card x Scale factor
Width of the largest complete enlargement = 5 in. x 2.2
Calculating the dimensions:
Length of the largest complete enlargement = 13.2 in.
Width of the largest complete enlargement = 11 in.
Therefore, the dimensions of the largest complete enlargement you can make on the piece of paper are 13.2 in. by 11 in.