Question

The ratio of sides of 2 similar triangles is 3:4. Find the ratio of their areas.

• A. $3:4$
• B. $4:3$
• C. $9:16$
• D. $16:9$

Answer 1

The correct option is C $9:16$

If two triangles are similar, it's bases and heights are in the same ratio.
If their sides are in the ratio $3:4$, their heights are also in the ratio $3:4.$
Area $=\frac{1}{2}bh$
So, ratio of the areas of those triangles $=\frac{\frac{1}{2}\times b_1\times h_1}{\frac{1}{2}\times b_2\times h_2}=\frac{3}{4}\times \frac{3}{4}=\frac{9}{16}$