A rectangular school banner has a length of 36 inches and a width of 52 inches. A sign is made that is similar to the school banner and has a length of 22 inches. What is the ratio of the area of the school banner to the area of the sign?

What is the ratio of the areas?

I tried doing 52/36 and multiplying that by 22. Then I tried getting the area by multiplying 22 and that number but I don't think its right.

Sign: W = 22/36 * 52 = 32.

Ab/As = (36*52)/(22*32) = 2.68.

Or Ab/As = (36/22)^2 = 2.68.

To find the ratio of the areas of the school banner and the sign, we first need to determine the areas of both.

The area of a rectangle can be calculated by multiplying its length by its width.

For the school banner, the length is 36 inches, and the width is 52 inches. Therefore, the area of the school banner is 36 inches * 52 inches = 1,872 square inches.

For the sign, the length is 22 inches. Since it is similar to the school banner, we can use the concept of similarity to find the corresponding width.

Similar figures have proportional sides. In this case, the school banner and the sign are similar rectangles, so the ratios of their corresponding sides should be equal.

The ratio of the length of the school banner to the length of the sign is 36 inches / 22 inches = 1.636.

To find the width of the sign, we can multiply the length of the sign by this ratio: 22 inches * 1.636 = 35.992 inches. Rounded to the nearest inch, the width of the sign is 36 inches.

Now that we have the dimensions of both the school banner and the sign, we can calculate the area of the sign. The area of the sign is 22 inches * 36 inches = 792 square inches.

Finally, we can find the ratio of the areas by dividing the area of the school banner by the area of the sign: 1872 square inches / 792 square inches = 2.36.

Therefore, the ratio of the area of the school banner to the area of the sign is 2.36:1.