Question

Item 20 A rectangular school banner has a length of 48 inches and a width of 30 inches. A sign is made that is similar to the school banner and has a length of 15 inches. What is the ratio of the area of the school banner to the area of the sign?

Answer 1

The ratio of the area of the school banner to the area of the sign is 256 : 25

Explanation:

The school banner has a length of 48 inches and a width of 30 inches.

Suppose, the width of the sign is
`x` inch.

Given that, the sign is similar to the school banner and has a length of 15 inches.

So, according to the ratio of length and width, the equation will be......

`(48)/(30)= (15)/(x) \\ \\ 48x=30*15=450\\ \\ x=(450)/(48)=9.375`

So, the width of the sign is 9.375 inches.

Formula for area of rectangle is:
`(length* width)`

So, the area of the school banner
`=(48* 30)inch^2= 1440 inch^2`

and the area of the sign
`=(15* 9.375)inch^2 = 140.625 inch^2`

Thus, the ratio of the area of the school banner to the area of the sign will be:
`(1440)/(140.625)= (256)/(25)=256:25`