Question

The areas of two similar triangles are $9c{m}^{2}and16c{m}^2$ respectively . The ratio of their corresponding sides is ____.

• A. 3: 4
• B. 4: 3
• C. 2: 3
• D. 4: 5

Answer 1

The correct option is A

3: 4

For similar triangles,
$\frac{\text{Area of tiangle1}}{\text{Area of tiangle2}}=\frac{{\text{(Corresponding length of tiangle1)}}^2}{{\text{(Corresponding length of tiangle2)}}^2}$

$\frac{Area\left({\Delta }_1\right)}{Area\left({\Delta }_2\right)}=\frac{(S_1{)}^2}{(S_2{)}^2}\frac{(S_1{)}^2}{(S_2{)}^2}=\frac{9}{16}=\sqrt{\frac{9}{16}}\frac{S_1}{S_2}=\frac{3}{4}=3:4$