MATH SOLVE

4 months ago

Q:
# 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 4inB. The scale factor is greater than 1 so the scale drawing is an enlargement, and the original card is 3 3/4in by 6 1/4inC. The scale factor is a fraction so the scale drawing is an reduction, and the original card is 2in by 4inD. 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

Accepted Solution

A:

Answer:The correct option is A.Step-by-step 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 [tex]2\frac{1}{2}[/tex] in by 5 in rectangle. Multiply each dimension by reciprocal of scale factor to find the dimension of original card.[tex]a=2\frac{1}{2}\times \frac{4}{5}=\frac{5}{2}\times \frac{4}{5}=2[/tex][tex]b=5\times \frac{4}{5}=4[/tex]The dimension of original card is 2 in by 4 in.Therefore the correct option is A.