What is the value of x? Enter your answer in the box. x = A triangle with midsegment parallel to the base. the right side of the triangle is labeled 121 cm below the midsegment and 11 cm above the midsegment. the right side of the triangle is labeled 5 x plus 10 below the midsegment and 10 cm above the midsegment.

A midsegmnet parallel to the the base will create two similar triangles, as shown in the figure. We know that in similar triangles the ratios of the lengths of their corresponding sides are equal; therefore, we can establish a ratio between the longer and the shorter sides of our triangles and solve for x as follows: 
[tex] \frac{11+121}{11} = \frac{10+5x+10}{10} [/tex]
[tex] \frac{132}{11} = \frac{5x+20}{10} [/tex]
[tex](10)(132)=(11)(5x+20)[/tex]
[tex]1320=55x+220[/tex]
[tex]55x=1100[/tex]
[tex]x= \frac{1100}{55} [/tex]
[tex]x=20[/tex]

The answer is x=20.