Question

If two similar triangles have a scale factor of $a:b$, then the ratio of their areas is:

• A. $a:b$
• B. $a^2:b^2$
• C. $a^3:b^3$
• D. None of these

Answer 1

The correct option is B $a^2:b^2$

We know if triangles are similar then the ratio of their areas is equal to square of ratio of their sides.

Given ratio of sides $=\frac{a}{b}$

$\therefore$ ratio of their areas $={\left(\frac{a}{b}\right)}^2=\frac{a^2}{b^2}$

So option $B$ is correct.