Chapter 11.7, Problem 8WE

To determine

To Find: The scale factor and ratio of perimeter.

Answer to Problem 8WE

Scale factor: $\sqrt{2}:1$

Ratio of perimeter: $\sqrt{2}:1$

Explanation of Solution

Given: Ratio of areas is $2:1$

If two similar triangles have ratio of area is $a^2:b^2$ .

Then the ratio of perimeter and scale factor is same i.e. $a:b$ .

Here

  $\begin{array}{l}{a}^2:b^2=2:1\\ a=\sqrt{2}\\ b=1\end{array}$

Thus

Scale factor is $\sqrt{2}:1$ .

Ratio of perimeter is $\sqrt{2}:1$ .