Answer:
The missing length is 12
Step-by-step explanation:
Required
Determine the missing length (LS)
If RS = 28 and KS = 14
Then
[tex]KR = RS - KS[/tex]
[tex]KR = 28 - 14[/tex]
[tex]KR = 14[/tex]
The sides of the given shape are directly proportional.
This implies that:
[tex]KS : LS = RS : QS[/tex]
[tex]KS = 14[/tex]
[tex]RS = 28[/tex]
[tex]QS = 12 + LS[/tex]
[tex]LS = ??[/tex]
So, the expression becomes:
[tex]14 : LS = 28 : 12 + LS[/tex]
Represent as a fraction
[tex]\frac{14}{LS} = \frac{28}{12 + LS}[/tex]
Cross Multiply:
[tex]14(12 + LS) = 28 * LS[/tex]
Divide through by 12
[tex]12 + LS = 2 * LS[/tex]
[tex]12 + LS = 2 LS[/tex]
Collect Like Terms
[tex]2LS - LS = 12[/tex]
[tex]LS = 12[/tex]
The length of the missing side is 12
