Question

The areas of two equilateral triangles are 27 yd2 and 75 yd2. Find the ratio of their perimeters.

Answer 1

If the areas of two equilateral triangles are 27 yd² and 75 yd², then the ratio of these areas is 27/75 = 9/25 

If the ratios of the areas are 9:25, then their similarity ratio and the ratio of their perimeters is √9:√35 = 3:5. 

3 : 5; 3 : 5 <==ANSWER 

Answer 2

Answer:

3:5

Step-by-step explanation:

The areas of two equilateral  triangles are 27 square yards and 75 square yards.

The area of an equilateral triangle with sides length 'a' is given by

$\frac{\sqrt3}{4}a^2$

Therefore, we have

$\frac{\frac{\sqrt3}{4}a_1^2}{\frac{\sqrt3}{4}a_2^2}=\frac{27}{75}\\\\\frac{a_1}{a_2}=\frac{3\sqrt3}{5\sqrt3}$

Now, multiply and divide both sides by 3

$\frac{3a_1}{3a_2}=\frac{9\sqrt3}{15\sqrt3}\\\\\frac{P_1}{P_2}=\frac{9}{15}\\\\\frac{P_1}{P_2}=\frac{3}{5}$

Hence, the ratio of perimeters of the given two equilateral triangles is 3:5