Question

Beth is designing a business card. She makes a scale drawing of her old business card by using the scale factor 5/4. Her scale drawing is 2 1/2in by 5in rectangle.

The print shop says the scale drawing is a reduction of the original card because the original card must be 3 1/8in by 6 1/4in. Which explains the print shop’s error?


A. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 2in by 4in


B. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 3 3/4in by 6 1/4in


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


D. The scale factor is a fraction so the scale drawing is an reduction, and the original card is 3 3/4in by 6 1/4in

Answer 1

Answer: A

Explanation:

Answer 2

The correct option is A.

Explanation:

It is given that Beth makes a scale drawing of her old business card by using the scale factor 5/4.

If the scale factor is less than 1, then it represents compression and if the scale factor is greater than 1, then it represents enlargement.

Since the scale factor is greater than 1 so the scale drawing is an enlargement.

Let the initial dimension of business card is a by b.

Her scale drawing is
`2(1)/(2)` in by 5 in rectangle. Multiply each dimension by reciprocal of scale factor to find the dimension of original card.

`a=2(1)/(2)* (4)/(5)=(5)/(2)* (4)/(5)=2`

`b=5* (4)/(5)=4`

The dimension of original card is 2 in by 4 in.

Therefore the correct option is A.