Question

Beth is designing a business card. She makes a scale drawing of her old business card by using a scale factor of Five-fourths. Her scale drawing is a 2 and one-half-inch by 5-inch rectangle. The print shop says that the scale drawing is a reduction of the original card because the original card must be 3 and StartFraction 1 over 8 EndFraction inches by 6 and one-fourth inches. Which explains the print shop's error and gives the correct dimensions of Beth's original card?

Answer 1

C. The scale factor is a fraction so the scale drawing is a reduction, and the original card is 2 inches by 4 inches.

Explanation:

Answer 2

The width and length of the old card are 2 inches and 4 inches respectively.

Explanation:

The given scale factor,
`C=(5)/(4)`

She draws is a rectangle by using the scale factor of C.

The width of her drawing,
`b=2(1)/(2)`
`=(5)/(2)` inch, and

the length of the drawing,
`a=5` inch.

Let
`a'` and
`b'` be the length and width of her reference business card (the old one as mentioned).

`\text{Scale factor}=\frac{\text{New dimension}}{\text{Reference dimention}}`

Here, the dimension is the length of the sides of rectangular cards.

So,
`C=(a)/(a')` and
`C=(b)/(b')`

`\Rightarrow (5)/(4)=(5)/(a')`

`\Rightarrow a'=4` inch

and
`(5)/(4)=(5/2)/(b')`

`\Rightarrow b'=2` inch

So, the old business card is of the dimensions 2 inches by 4 inches, which are the correct dimensions.

Actually, the print shop multiplied he scale-factor, C, with the new scaled length to get the reference length (lengths of original old card), which was the error. In, fact, as already described earlier, the new dimensions can be obtained by multiplying the scale-factor, C, with the reference dimensions.