Question

the areas of two similar squares are \\(16\text{ m}^2\\) and \\(49\text{ m}^2\\). what is the scale factor of their side lengths?

?:

Explanation:

Relate area ratio to scale factor

$$ \frac{A_1}{A_2} = k^2 = \frac{16}{49} $$

Solve for the scale factor

$$ k = \sqrt{\frac{16}{49}} = \frac{4}{7} $$

Express as a ratio

$$ 4:7 $$

Answer:

The areas of two similar squares are \(16\text{ m}^2\) and \(49\text{ m}^2\). What is the scale factor of their side lengths?

<blank>4</blank> : <blank>7</blank>