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# Algebra 1 Item No 80

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### Algebra 1 Item No 80

1. 1. Algebra 1 Item No. 80 (ch5-9) <ul><li>A rectangle land made with length 20 meters, width 10 meters. A road of equal width is made to surround the land and has the area of 136 square meters. Find the width of the road. </li></ul><ul><li>A. 2 m C. 17 m </li></ul><ul><li>B. both A and B D. none of these </li></ul>www.upcatreview.com
2. 2. <ul><li>To solve the problem, we must first visualize the given situation: </li></ul>LOT ROAD www.upcatreview.com 20 m 10 m x L W
3. 3. <ul><li>We know that the area of the road is given: </li></ul><ul><li>A road = 136 m 2 </li></ul>LOT ROAD A = 136 m 2 www.upcatreview.com 20 m 10 m x L W
4. 4. <ul><li>Because the length and width of the lot is given, we can compute the area of the lot: </li></ul><ul><li>A lot = (10 m)(20 m) = 200 m 2 </li></ul>LOT ROAD A = 136 m 2 A = 200 m 2 www.upcatreview.com 20 m 10 m x L W
5. 5. <ul><li>The total area can be found by combining the area of the road and the area of the lot. </li></ul><ul><li>A Total = A lot + A road (eqn 1) </li></ul><ul><li> A Total = 200 + 136 = 336 m 2 </li></ul>www.upcatreview.com
6. 6. <ul><li>The total area can be found by combining the area of the road and the area of the lot. </li></ul><ul><li>A Total = A lot + A road (eqn 1) </li></ul><ul><li> A Total = 200 + 136 = 336 m 2 </li></ul><ul><li>Using the representation in our given figure, the total area is: </li></ul><ul><li> A Total =L  W (eqn 2) </li></ul>www.upcatreview.com
7. 7. <ul><li>From the figure, we can represent the length L as L = 20 – 2x and the width as W = 10 – 2x </li></ul>www.upcatreview.com 20 m 10 m x L W
8. 8. <ul><li>From the figure, we can represent the length L as L = 20 – 2x and the width as W = 10 – 2x </li></ul>L = 20 – 2x W = 10 – 2x www.upcatreview.com 20 m 10 m x L W
9. 9. <ul><li>We can now have the equation for the total area: </li></ul>www.upcatreview.com
10. 10. <ul><li>Substituting the given information into the equation 1, we have: </li></ul>www.upcatreview.com
11. 11. <ul><li>Substituting the given information into the equation 1, we have: </li></ul><ul><li>We now have a quadratic equation: </li></ul>www.upcatreview.com
12. 12. <ul><li>We obtained two values for x, </li></ul><ul><li>x = – 17 and x = 2 </li></ul><ul><li>However, logic tells us that we cannot have a negative value for distance so we reject the solution – 17. The only accepted value for the road’s width is: </li></ul><ul><li>x = 2 </li></ul>www.upcatreview.com
13. 13. <ul><li>The answer is: </li></ul><ul><li>A. 2 m </li></ul>www.upcatreview.com
14. 14. Algebra 1 Item No. 80 (ch5-9) <ul><li>A rectangle land made with length 20 meters, width 10 meters. A road of equal width is made to surround the land and has the area of 136 square meters. Find the width of the road. </li></ul><ul><li>A. 2 m C. 17 m </li></ul><ul><li>B. both A and B D. none of these </li></ul>www.upcatreview.com