Question

You originally draw a design for an art contest on a 3 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.

Answer 1

The answer is 6.3

3 / 5 = x / 10.5
x = 6.3

Answer 2

Since the drawings are similar, the lengths of the 2 sides are proportional.

Since the largest size is 10.5 for the new drawing, it corresponds to the large side of the former drawing, which is 5.

Similary, the corresponding side of 3 (in the former drawing) in the larger drawing is what we are seeking to find, let's call this x.

So the ratio of 10.5 is to 5 should be equal to the ratio of x is to 3. Setting up the ratio, we have:

$\frac{10.5}{5}= \frac{x}{3}$

Now cross multiply and solve for x, we get:

$\frac{10.5}{5}= \frac{x}{3} \\3*10.5=5x\\31.5=5x\\\frac{31.5}{5} =x\\6.3=x$.

So the length of the side we are looking for in the former drawing is 6.3 inches.

ANSWER: 6.3 in