SOLUTION: Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 300 square feet of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 300 square feet of       Log On


   

Question 1066615: Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 300 square feet of carpeting. What dimensions should the rug​ have? The dimensions of the rug should be
blank ft.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the width of the border
around the rug. The width and length
both get increased by +2x+
+%28+18+-+2x+%29%2A%28+31+-+2x+%29+=+300+
+558+-+62x+-+36x+%2B+4x%5E2+=+300+
+4x%5E2+-+98x+%2B+258+=+0+
+2x%5E2+-+49x+%2B+129+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-49+
+c+=+129+
+x+=+%28-%28-49%29+%2B-+sqrt%28%28-49%29%5E2+-+4%2A2%2A129+%29%29+%2F+%282%2A2%29+
+x+=+%28+49+%2B-+sqrt%28+2401+-+1032+%29%29+%2F+4+
+x+=+%28+49+%2B-+sqrt%28+1369+%29%29+%2F+4+
+x+=+%28+49+-+37+%29%2F4+ ( the negative square root works here )
+x+=+12%2F4+
+x+=+3+
-----------------
+%28+18+-+2x+%29%2A%28+31+-+2x+%29+=+300+
+18+-+2x+=+18+-+2%2A3+
+18+-+2x+=+18+-+6+
+18+-+2x+=+12+
and
+31+-+2x+=+31+-+2%2A3+
+31+-+2x+=+25++
----------------------------
The dimensions of the rug are 12 x 25
check:
+12%2A25+=+300+
OK