Question

The areas of two similar triangles are $49{cm}^2$ and $64{cm}^2$ respectively. The ratio of their corresponding sides is:

• A. $49:64$
• B. $7:8$
• C. $64:49$
• D. none of these

Answer 1

The correct option is B $7:8$

Areas of two similar triangles are $49$ cm ${}^2$ and $64$ cm ${}^2.$
For similar triangles the ratio of areas is equal to the ratio of square of corresponding sides.
Hence, $\frac{A_1}{A_2}=\frac{(s_1{)}^2}{(s_2{)}^2}$
$⟹\frac{49}{64}=\frac{(s_1{)}^2}{(s_2{)}^2}$
$⟹\frac{s_1}{s_2}=\frac{7}{8}$