Given:
The areas of two similar squares are 16m² and 49m².
To find:
The scale factor of their side lengths.
Solution:
We know that the ratio of the areas of the similar squares is proportional to the ratio of square of there sides.
[tex]\dfrac{\text{Area of first square}}{\text{Area of second square}}=\dfrac{(\text{Side length of first square})^2}{(\text{Side length of second square})^2}[/tex]
[tex]\dfrac{16\ m^2}{49\ m^2}=\dfrac{s_1^2}{s_2^2}[/tex]
[tex]\dfrac{4^2}{7^2}=\left(\dfrac{s_1}{s_2}\right)^2[/tex]
[tex]\left(\dfrac{4}{7}\right)^2=\left(\dfrac{s_1}{s_2}\right)^2[/tex]
Taking square root on both sides, we get
[tex]\dfrac{4}{7}=\dfrac{s_1}{s_2}[/tex]
[tex]\dfrac{s_1}{s_2}=\dfrac{4}{7}[/tex]
Now, the scale factor is the ratio of side length of second square to the side length of first square.
[tex]k=\dfrac{s_2}{s_1}[/tex]
[tex]k=\dfrac{7}{4}[/tex]
Therefore, the scale factor of their side lengths is [tex]k=\dfrac{7}{4}[/tex].
