Question

The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

• A. $625:256$
• B. $5:6$
• C. $25:16$
• D. $5:4$

Answer 1

The correct option is D $5:4$

The ratio of areas of given similar triangles $=25:16$

And we know that, ratio of areas of two triangles is same as the ratio of squares of their corresponding sides
$\therefore$ Ratio of the corresponding sides of the similar triangles $=\sqrt{\frac{25}{16}}=\frac{5}{4}=5:4$
$\therefore$ The ratio of the perimeters of given similar triangles $=5:4$

Hence, the answer is $5:4$.