Question

Since all squares are similar, then the ratio of one square’s side to perimeter is proportional to any other’s. If the side of a square of fabric is 2 yards, then the perimeter is 8 yards. Use a proportion to determine the perimeter of a square with a side 9 yards long. Write your final answer in a complete sentence.
Please help and explain ur answer CX

Answer 1

You are told that a square with a side of 2 yards has a perimeter of 8 yards. So we can think of it as side/perimeter = 2/8.

You are also reminded that all squares are similar (they have the same shape, their corresponding angles are congruent and their sides are in proportion) and that as such if we compare the ration of their side to their perimeter (side/perimeter) it is always the same. We know it will be 2/8.

We can use a proportion (two fractions set equal to each other) to highlight the ratio of the sides to the perimeter. It is:

$\frac{side}{perimeter} = \frac{2}{8}$

Now you are asked to find the perimeter of a square whose side is 9yards using this proportion. You can do this by replacing the word "side" with 9 and solving for perimeter. To make it easier let's write p for perimeter. We get:

$\frac{9}{p} = \frac{2}{8}$

Recall that proportions can be solved by cross multiplying. So let's cross-multiply and solve for p.

$\frac{9}{p} = \frac{2}{8}$
$2p=72$
$p=36$

Therefore the perimeter is 36 yards.

Answer 2

The perimeter is 36 yd.

We set up a proportion to represent this situation.  We know that the ratio of the side to the perimeter is the same for every square.  This means that the ratio of the first square, 2/8 is the same for the second one.  We know that the side length is 9, which gives us:

2/8 = 9/x

Cross multiply:
2*x = 8*9
2x = 72

Divide both sides by 2:
2x/2 = 72/2
x = 36