Question

The ratio of the perimeters of two rectangles is 4 to 9. The perimeter of the larger rectangle is 54 inches. What is the perimeter of the smaller rectangle?

Answer 1

awh, ratios, these are my favorite
so we could write it like this-
Triangle Large Perimeter 54: is to the ratio of the 9
or better said
54 is to 9
54:9

in this case, i know that the 9 or the 4 had to go to 54, but how to choose depended on the information that 54 was said to be the 'larger triangle'

and ratios can be written like this-
54:9 or
54/9 or

9:54 or
9/54
mmm k?

so, i'll write it in a fraction and set one triangles properties equal to the other, like this
\[\frac{ 54 }{ 9 } = \frac{ ? }{ 4 }\]

Answer 2

it doesn't matter if the fractions are flipped or not, BUT what does matter is that if perimeter of one triangle is in the numerator, then the perimeter of the other triangle must be in the neumerator also!