Item 20 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

The ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.

Step-by-step explanation:

Given:

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.

Now, to find the ratio of the area of the school banner to the area of the sign.

Dimensions of school banner :

Length = 54 inches.

Width = 36 inches.

Dimension of school sign:

Length = 17 inches.

So, to we find the width of sign by using cross multiplication method:

Let the width be

So, 54 is equivalent to 36.

Thus, 17 is equivalent to

By cross multiplying we get:

Dividing both sides by 54 we get:

Thus, the width of sign = 11.33 inches.

Now, to get the ratio of the area of the school banner to the area of the sign:

Area of the school banner : Area of the school sign.

=

=

Therefore, the ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.

The ratio of the area of the school banner to the area of the sign is 1944 : 192.61.

Step-by-step explanation:

Given:

Length of the School banner = 54 inches

width of the school banner = 36 inches

Length of the sign = 17 inches

We need to find the ratio of the area of the school banner to the area of the sign

Solution:

First we will find the width of the sign.

Let the width of the sign be

Now we know that;

When two rectangles are similar to each other then their ratio of the dimension are equal.

so we can say that;

By using Cross multiplication we get;

Now we will find the Area.

Area of school banner is equal to length of the school banner times width of the school banner.

framing in equation form we get;

Area of school banner =

Area of the sign is equal to length of the sign times width of the sign.

framing in equation form we get;

Area of the sign =

Now we will find the ratio of the area of the school banner to the area of the sign.

Hence The  ratio of the area of the school banner to the area of the sign is 1944:192.61.

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