Dimensions of a rug

Question

Cynthia Besch wants to buy a rug for a room that is 25ft wide and 33ft long . She wants to leave a uniform strip of floor around the rug. She can afford to buy 609 square feet of carpeting. What dimensions should the rug have ?

Answer 1

Hello,

The answer is below:

Cynthia's room Area= 25 ft wide x 33 feet long=825 feet square. She wants to leave a uniform strip of floor all around the rug and has affordability to buy 609 square feet of carpet. So in order to figure the dimensions of the rug, try the following:

A 2 feet space around the rug would be = 31 (33-2) x 23 (25-2)=713 square feet. However, she only can buy 609 square feet of carpet. So a 2 feet space around carpet is not correct. Keep deducing,

A 3 feet space around the rug would be= 30 (33-3) x 22 (25-3)=660 square feet. But 660 square feet rug exceeds Cynthia's ability to only buy 609 square feet of carpet.

A 4 feet space around the rug would be=29 (33-4) x 21 (25-4)=609 square feet which matches Cynthia's ability to buy 609 square feet of rug. Hence, the dimensions of the rug would be 29 feet long and 21 feet wide with a 4 foot space around the carpet uniformly.

Hope this was easy for you to deduce. Thanks,