Answer
The missing length is 10
Step-by-step explanation:
Represent the missing length with x
The sides of the given shape are directly proportional.
Mathematically:
(15 + x) to (12 + 8) and x to 7
Represent as a ratio:
[tex](15 + x) : (12 + 8) = x : 8[/tex]
[tex]15 + x : 20= x : 8[/tex]
Convert to fraction
[tex]\frac{15 + x}{20} = \frac{x}{8}[/tex]
Cross Multiply:
[tex](15 + x)*8 = 20 * x[/tex]
[tex]120 + 8x = 20x[/tex]
Collect Like Terms
[tex]20x - 8x = 120[/tex]
[tex]12x = 120[/tex]
Solve for x
[tex]x = \frac{120}{10}[/tex]
[tex]x = 10[/tex]
The length of the missing side is 10
