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+x-2)=0

2(x+2)(x-1)=0

Solve for x and reject the root that is negative.

- algebra-correction -
**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+x-12)=0

2(x-3)(x+4)=0

Solve for x and reject the root that is negative.

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