SOLUTION: Cynthia Besch wants to buy a rug for a room that is 14 ft wide and 29 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 250 square feet of

Question 1049572: Cynthia Besch wants to buy a rug for a room that is 14 ft wide and 29 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 250 square feet of carpeting. What dimensions should the rug have?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
w, uniform width of floor around the rug

Area of the room, 14*29
Area of the border around the rug, 14*29-(14-2w)(29-2w)
Area of just the rug, (14-2w)(29-2w)
Area of just the rug is also given, 250 square feet.

This description is easily generalized. See this instructive video:
rectangular inside-border of uniform width - video
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Cynthia Besch wants to buy a rug for a room that is 14 ft wide and 29 ft long.
She wants to leave a uniform strip of floor around the rug. She can afford to buy 250 square feet of carpeting.
What dimensions should the rug have?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let me show you another way of solving, without quadratic equations. Notice that the difference "the length - the width" is 29-14 = 15 ft. Since there is a uniform strip of floor around the rug, the difference of dimensions of the rug is the same, 15 ft. Thus you need to determine the dimensions that have the difference of 15 and the product of 250 (square feet). Can you guess them? - But of course, 25 x 10. Answer. The rug should be 25 X 10 ft.

But if you want to know how to solve similar problems WITH equations, see the lesson
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook.

RELATED QUESTIONS
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants... (answered by josmiceli)
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants... (answered by ikleyn,jorel1380)
cynthia besch wants to buy a rug for a room that is 12 ft wide and 15 ft long. she wants... (answered by mananth)
Cynthia Besch wants to buy a rug for a room that is 11 ft. wide and 30 ft. long. She... (answered by ankor@dixie-net.com)
Cynthia Besch wants to buy a rug for a room that is 17 ft wide and 24 ft long. She wants... (answered by Theo)
Cynthia Besch wants to buy a rug for a room that is 22 ft wide and 27 ft long.... (answered by ikleyn)
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 19 ft long. She wants... (answered by jorel1380)
Cynthia Besch wants to buy a rug for a room that is 23 ft wide and 24 ft long. She wants... (answered by josgarithmetic,ikleyn)
Cynthia Besch wants to buy a rug for a room that is 26 ft wide and 27 ft long. She wants... (answered by josgarithmetic,ikleyn)