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.

Is the answer 4.2 or 8.4? or something else entirely

Answer 1

If the 5” dimension is expanded to 10.5” the scaling factor is 10.5/5=2.1. When this is applied to the 3” dimension it becomes 6.3”.

Answer 2

we have that

The dimensions of the originally draw are
`3\ in\ x\ 5\ in`

we know that

If the two drawings are similar

then

the ratio of the corresponding sides are equals

so

`(10.5)/(5)= (x)/(3) \\ \\5x=10.5*3 \\ \\x=6.3\ in`

therefore

the answer is

the length of the other dimension is
`6.3\ in`