There are two similar rectangles. The ratio of their areas is 4:9. What is the ratio of their perimeters?

Question

My question is There are two similar rectangles. The ratio of their areas is 4:9. What is the ratio of their perimeters? 

Answer 1

We are given that the rectangles are similar, that is l₁/l₂ = w₁/w₂, or, for later use that l₁/w₁ = l₂/w₂   and that the ratio of their areas is 4/9.

That is l₁w₁/(l₂w₂) = 4/9.   Using the first equation, in the second, we have since  l₁/l₂ = w₁/w₂

l₁w₁/(l₂w₂) = w₁²/w₂² = 4/9 or that w₁/w₂ = 2/3, which is also l₁/l₂.  The ratio of their perimeters is

(l₁ + w₁)/(l₂  + w₂) = ((l₁/w₁) + 1)/((l₂/w₂) + 1)×(w₁/w₂) = w₁/w₂ = 2/3.

Answer 2

Area is = L*W 

Perimeter = 2L + 2W

 

The keyword in this statement is that they are similar rectangles. 

 

We can give any values for one rectangle, but have to give a proportional value for the other. 

 

The sides of first rectangle could be 2 by 2. This will give an area of 4.

The sides of second could be 3 by 3. This will give an area of 9.

 

The two are proportional.

 

Now we go to the Perimeter. 

2(2)+2(2)= 8

This is the perimeter of first rectangle. 

 

2(3)+2(3)= 12

This is the perimeter of the second. 

 

So the answer is 8:12

If you want to simply your answer, it would be 2:3