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# C:\Documents And Settings\Jessica Hanson\Desktop\Border+Problems

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### C:\Documents And Settings\Jessica Hanson\Desktop\Border+Problems

1. 1. Border Problems
2. 2. Example <ul><li>The Smiths have decided to put a paved walkway of uniform width around their swimming pool. The pool is a rectangular pool that measures 12 feet by 20 feet. The area of the walkway will be 68ft^2 find the width of the walkway. </li></ul>
3. 3. Step 1 <ul><li>First it is important to draw a diagram of the problem </li></ul>
4. 4. Step 2 <ul><li>There are three rectangles in this diagram we need to look at: the large rectangle, the pool, and the rectangle that stands for the walkway around the pool. </li></ul>
5. 5. Step 3 <ul><li>The length of the larger rectangle is 20+x+x in other words, 20+2x. The width of the larger rectangle is 12+x+x in other words, 12+2x. </li></ul>
6. 6. Step 3 continued… <ul><li>The area for the larger rectangle then becomes (20+2x)(12+2x). </li></ul><ul><li>The pool has an area of (20)(12)=240ft^2 </li></ul>
7. 7. Step 4 <ul><li>The rectangle that wraps around the pool is 68ft^2. By putting all three of these areas together, we know that the area of the larger rectangle is the same as the area of the pool plus the area of the walkway that surrounds the pool. The equation becomes: (20+2x)(12+2x)=68+240 </li></ul><ul><li>(The 240 comes from the area of the pool.) </li></ul>
8. 8. Step 5 <ul><li>Now its time to solve the equation! </li></ul><ul><li>Organize the terms so that its easier to put them into the area model, and add 68+240. </li></ul><ul><li>The equation is now: (2x+20)(2x+12)=308 </li></ul>
9. 9. Step 6 <ul><li>Use the area model to multiply out the two binomials. </li></ul><ul><li>Your equation is now 4x^2+64x+240=308 </li></ul><ul><li>Subtract 308 from both sides. </li></ul><ul><li>Your equation: 4x^2+64x-68=0 </li></ul>
10. 10. Step 7 <ul><li>Factoring time! </li></ul><ul><li>4x+64x-68=0 now factors into: </li></ul><ul><li>4(x+17)(x-1)=0 </li></ul><ul><li>x=-17, x=1 </li></ul><ul><li>Widths around a pool cannot be negative, so the answer for the width of the walkway is 1. </li></ul>