exam Maths Puzzle Numerical Ability

The ancient Greeks thought that the most pleasing shape for rectangle was one for which the ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimention would the length and width have the golden ratio?

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The algebra questions reads the square root of x minus 8 is equal to the square root of 13 plus x. Please help me solve this! What makes a number real, whole,natural, interger, irratiional, rational?