Question

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.

Answer 1

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.

Answer 2

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.