Posted by Anonymous on Saturday, June 12, 2010 at 9:51pm.
The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions of the rectangle in centimeters? Enter your answers in the blanks. Enter only the numeric values rounded to the nearest tenth.

algebra  MathMate, Saturday, June 12, 2010 at 10:18pm
Let x be the short side, then the long side is (x+1).
By Pythagoras theorem, the diagonal is
√(x²+(x+1)²)
=&radic(2x²+2x+1)=5
Square both sides to get
2x²+2x+1 = 5
2(x²+x2)=0
2(x+2)(x1)=0
Solve for x and reject the root that is negative.

algebracorrection  MathMate, Sunday, June 13, 2010 at 9:22am
Sorry, there was a mistake in the above solution. Here's the corrected version.
√(x²+(x+1)²)
=√(2x²+2x+1)=5
Square both sides to get
2x²+2x+1 = 25
2(x²+x12)=0
2(x3)(x+4)=0
Solve for x and reject the root that is negative.
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