Answer:
x = 8
Step-by-step explanation:
The diagram shows two similar triangles. Similar triangles have all the same angles and the sides are proportional to one another. So, by setting up a proportion of the sides, you can solve for the missing variable:
[tex]\frac{bigger}{smaller}=\frac{156}{72}=\frac{(14x+5)}{54}[/tex]
Cross-multiply: 72(14x + 5) = 156(54)
Distribute: 1008x + 360 = 8424
Subtract 360 from both sides: 1008x + 360 - 360 = 8424 - 360
Divide: 1008x/1008 = 8064/1008
Solve for x: x = 8
