Question

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

Answer 1

Answer:

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 $x.$

So, 54 is equivalent to 36.

Thus, 17 is equivalent to $x.$

$\frac{54}{36} =\frac{17}{x}$

By cross multiplying we get:

$54x=612$

Dividing both sides by 54 we get:

$x=11.33\ inches.$

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.

= $54\times 36:17\times 11.33$

= $1944:192.61$

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

Answer 2

Answer:

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 $(l_1)$ = 54 inches

width of the school banner $(w_1)$ = 36 inches

Length of the sign $(l_2)$ = 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 $w_2$

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;

$\frac{l_1}{l_2}=\frac{w_1}{w_2}\\\\\frac{54}{17}=\frac{36}{w_2}$

By using Cross multiplication we get;

$w_2=\frac{17\times36}{54} = 11.33\ in$

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 = $54\times36 = 1944 \ ft^2$

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 = $17\times11.33= 192.61\ ft^2$

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

$\frac{\textrm{Area of School Banner}}{\textrm{Area of the Sign}}=\frac{1944}{192.61}$

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