a) Both the length and the width of the rectangle are square roots of integers.
b) The length and the width of the rectangle are 6√5 units and 3√5 units, respectively.
<h3>How to analyze irrational numbers</h3>
Irrational numbers are numbers that not rational, that is, numbers that not of the form m / n, where m and n are integers and n is different of zero. Rational numbers may be integers or not.
Now, the statement indicates that the length and the width of rectangle have measures of 2 · x and x, respectively, and that the area of the rectangle is equal to 90 square units. The area formula is presented below:
90 = (2 · x) · x
90 = 2 · x²
x² = 45
x = √45
x = √(9 × 5)
x = √9 × √5
x = 3√5
a) Both the length and the width of the rectangle are square roots of integers.
b) The length and the width of the rectangle are 6√5 units (approx. 13.416 units) and 3√5 units (approx. 6.708 units), respectively.
To learn more on irrational numbers: brainly.com/question/3386568
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