Question

The areas of two smiley faces are in the ratio 10:1
The height of the larger face is 4cm. Calculate the height of the smaller face.

Answer 1

area goes with the square so if the ratio of the areas is \(10:1\) the ratio of the lengths is \(\sqrt{10}:1\)

Answer 2

\[\frac{x}{4}=\frac{1}{\sqrt{10}}\iff x=\frac{4}{\sqrt{10}}\]