anonymous
  • anonymous
the length of a new playing field is 7 yards longer than quadruple the width. if the perimeter of the rectangle playing field is 494 yards, what are the dimensions?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
So you're looking at the following: -------------------------- - - W - - - - -------------------------- L Where L is the length of the rectangle and W is the width, right? It says that the width is equal to 7 longer than 4 times the width, so the length is: L = 4W + 7 And that the perimeter is 494 yards. The perimeter for a rectangle is: P = 2L + 2W, and since we know L and P, we can plug them in, like so: 494 yards = 2(4W+7) + 2W. Now we solve for W. 494 yards = (8W + 14) + 2W which is equal to 10W + 14. 494 yards = 10W + 14 (subtract the 14 across and divide by ten and we'll get the width!) W = 48. Now we know that L = 4W+7, and W = 48, so L = 4(48) + 7 = 192+ 7 = 199 so the length is 199 yards and the width is 48 yards. You can verify this by using the perimeter formula to see if 494 = 2(48) + 2(199) and it does. Hope this helps!
anonymous
  • anonymous
Sorry that the rectangle got messed up! It didn't print the spacing properly, haha.

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