SOLUTION: a rectangle has a diagonal that measures 10 centimeter and a length that is 2 centimeter longer thatn the width. What is the width of the rectangle in cenitmeter? A 5 B 6 C 8

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Question 294591: a rectangle has a diagonal that measures 10 centimeter and a length that is 2 centimeter longer thatn the width. What is the width of the rectangle in cenitmeter?
A 5
B 6
C 8
D 12
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 where c = 10, a = L, and b = W
10%5E2+=+L%5E2%2BW%5E2 Substitute L+=+W%2B2
100+=+%28W%2B2%29%5E2%2BW%5E2
100+=+%28W%5E2%2B4W%2B4%29%2BW%5E2 Rearrange into a standard form for quadratice equations.
2W%5E2%2B4W-96+=+0 Factor 2.
2%28W%5E2%2B2W-48%29+=+0 so...
W%5E2%2B2W-48+=+0 Solve by factoring.
%28W-6%29%28W%2B8%29+=+0 Apply the "zero product" rule.
W-6+=+0 or W+%2B8+=+0 which means that...
W+=+6 or W+=+-8 Discard the negative solution.
W+=+6 This is the width of the rectangle.