Answer:
[tex]Area = 27.5[/tex]
Step-by-step explanation:
Given
[tex]J_{Area} = 440[/tex]
[tex]J_{Width} = 22[/tex]
[tex]K_{Width} = 5.5[/tex]
See attachment
Required
Determine the area of K
First, we need to calculate the length of the rectangle J
[tex]J_{Length} * J_{Width} = J_{Area}[/tex]
This gives:
[tex]J_{Length} * 22 = 440[/tex]
Divide both sides by 22
[tex]\frac{J_{Length} * 22}{22} = \frac{440}{22}[/tex]
[tex]J_{Length} = 20[/tex]
So, the length of the rectangle J is 20.
Since both shapes are similar, then:
[tex]J_{Length} : J_{Width} = K_{Length} : `K_{Width}[/tex]
Substitute the known values:
[tex]20 : 22 = K_{Length} : `5.5[/tex]
Express as fraction:
[tex]\frac{20 }{ 22 }= \frac{K_{Length} }{ `5.5}[/tex]
Make Length, the subject of formula
[tex]K_{Length} = \frac{5.5 * 20}{22}[/tex]
[tex]K_{Length} = \frac{110}{22}[/tex]
[tex]K_{Length} = 5[/tex]
The area of K is:
[tex]Area = K_{Length} * K_{Width[/tex]
[tex]Area = 5.5 * 5[/tex]
[tex]Area = 27.5[/tex]
