anonymous
  • anonymous
Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m2 by increasing the width and length by the same amount. What will be the width (shorter dimension) of the new garden? A. 13 m wide B. 14 m wide C. 15 m wide D. 16 m wide
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
you know what when i first got on here today i hade 9 medals now i have 45 lol
anonymous
  • anonymous
lol you deserve them all and more
anonymous
  • anonymous
how much did you have before the BIG test?

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anonymous
  • anonymous
sorry but what do you mean? c:
anonymous
  • anonymous
medal's
anonymous
  • anonymous
i think 60 something c:
anonymous
  • anonymous
nice
anonymous
  • anonymous
brb real quick
anonymous
  • anonymous
k i am back @pinkbubbles
anonymous
  • anonymous
one second
anonymous
  • anonymous
ok take your time
anonymous
  • anonymous
sorry
anonymous
  • anonymous
its fine. :)
mathstudent55
  • mathstudent55
The original gardens has these dimensions. |dw:1437601075655:dw|
mathstudent55
  • mathstudent55
|dw:1437601140143:dw|
mathstudent55
  • mathstudent55
The original garden has dimensions 13 m by 10 m. If you increase both the length and the width by x meters, what are the new length and width?
anonymous
  • anonymous
oh i know what it is 13m right ;)
mathstudent55
  • mathstudent55
|dw:1437601335029:dw|
mathstudent55
  • mathstudent55
Since the area of the new rectangle is length * width, we multiply x + 13 by x + 10. The new area is 208, so we set the new area equal to 208, and we solve for x. (x + 13)(x + 10) = 208 \(x^2 + 10x + 13x + 130 = 208\) \(x^2 + 23x - 78 = 0\) \((x - 3)(x + 26) = 0\) \(x - 3 = 0\) or \(x + 26 = 0\) \(x = 3 \) or \(x = -26\) Since the increase in length and width cannot be -26 m, it must be 3 m. The original width was 10 m. 10 m + 3 m = 13 m The new width is 13 m. Check: The width became 13 m, and the length became 13 m + 3 m = 16 m \((13 ~m)(16 ~m) = 208 ~m^2\) 13 m is correct.
mathstudent55
  • mathstudent55
Yes, you are correct.

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