The ratio of the areas of the two squares is 25 to 9. the side length of the smaller square is 30 meters. how long is the side length of the larger square. explain your reasoning

Let the area of the smaller square be a and that of the bigger square A

Let the length of the smaller square be l while that of the bigger square is L...

So let's analyse according to the question...

A:a = 25:9

A = L × L(bigger square)
a= l×l(smaller length)
l=30(as written in the question) So a= 30*30=900

A:900 = 25:9

L²:900 = 25:9

L²/900 = 25/9

Multiply both sides by 9 You'll have

L²/100 = 25

Cross multiply

L²=2500

L = 50(50*50=2500)

As a smart dude you'lld not need a long solution to solve this all you need do is to watch carefully...
The question says the ration of the area of the two squares is 25:9(definitely the bigger square takes 25 as it's divided ratio)..

You were given the length of the smaller square 30m (square this you'll have the area of the smaller square) 30*30=900
And the ratio of the bigger to small is 25:9
This means that a factor of 100 has been cancelled out from the ratios... If you add that factor back you'll have the area of the bigger square and when you find the square root you'll get the length of the bigger square

Hope this helped?