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?
sides have ratio 36/22
areas have ratio (36/22)^2
A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign?
17\54
To find the ratio of the areas, we need to find the area of both the school banner and the sign.
The area of the school banner can be found by multiplying its length by its width:
Area of the school banner = length * width = 36 inches * 52 inches
The area of the sign can be found by using the given length of the sign:
Area of the sign = length of the sign * width of the sign = 22 inches * unknown width
Since the sign is similar to the school banner, it means that the ratio of the length of the school banner to the length of the sign is equal to the ratio of the width of the school banner to the width of the sign:
Ratio of the length = 36 inches / 22 inches
Ratio of the width = 52 inches / unknown width
Since the ratio of the length is equal to the ratio of the width, we can set up an equation:
36 inches / 22 inches = 52 inches / unknown width
Solving this equation will give us the unknown width of the sign.
Once we have the width of the sign, we can substitute it into the formula to find the area of the sign.
Finally, we can take the ratio of the area of the school banner to the area of the sign to find the answer.