chaz draws a square with sides equal to 4 units, then he dilates the square so the sides are equal to 6 units. chaz writes a fraction in lowest terms to express the relationship between the area of the original square and the dilated square, with the numerator expressing the area of the dilated square. what is that fraction?

Answer 1

To find the areas of the squares and the fraction expressing the relationship between the areas, we’ll follow these steps:

1. Calculate the area of the original square:

   • The side length of the original square is 4 units.
   • Area of the original square = side length × side length = \(4 \times 4 = 16\) square units.

2. Calculate the area of the dilated square:

   • The side length of the dilated square is 6 units.
   • Area of the dilated square = side length × side length = \(6 \times 6 = 36\) square units.

3. Express the relationship as a fraction:

   • We want the fraction with the area of the dilated square as the numerator and the area of the original square as the denominator.
   • This gives us the fraction \(\frac{36}{16}\).

4. Simplify the fraction:

   • The greatest common divisor of 36 and 16 is 4.
   • Dividing both the numerator and the denominator by 4 gives us \(\frac{36 \div 4}{16 \div 4} = \frac{9}{4}\).

Therefore, the fraction that expresses the relationship between the area of the dilated square and the original square in lowest terms is \(\frac{9}{4}\).