Find the ratio of their perimeters.

Question

1. The ratios of the areas of two squares is 16:35. Find the ratio of their perimeters.

2. Two regular hexagons have side lengths in the ratio of 7:12. What is the ratio of the areas of the hexagons?

Answer 1

Aisha,

 

If you can answer 1 you can answer 2 and vice versa.

 

"The ratios of the areas of two squares is 16:35." Let us assume that area A1 = 16 unit². that makes area A2 = 35 unit².

This makes the side s1 = 4 and s2 = √35. And, by extension, makes the perimeters p1 = 4(4) units  and

p2 = 4(√35) umits.

 

Now, for the ratio of the perimeters p1:p2, we have 4(4):4(√35).

<=> p1:p2 = 4:√35  -------- (you don't change the proportion when you divide both sides by 4 and "units').

 

As for question 2, you now know that the ratio of areas is proportional to the square of the ratio sides.

I hope this helps