Answer:
By using the given information in the diagram, the value of x is 20.
Step-by-step explanation:
From looking at the diagram, the triangles appear to be similar. This means that they are going to have the same ratios between each side.
We are given two measurements on one side of the triangle, 11 and 121. We can find the ratio of these sides by dividing 121 by 11.
121 ÷ 11 = 11
So, the ratio between the two triangles is 11 which means that the ratio for the rest of the sides of the triangle is going to have a ratio of 11. Knowing this, we can turn this into a equation to find the value of x.
[tex]\frac{121}{11} = \frac{5x+10}{10}[/tex]
Cross multiply the terms.
1210 = 55x + 110
Subtract 110 from both sides of the equation.
1210 - 110 = 55x + 110 - 110
1100 = 55x
Divide 55 from both sides of the equation.
1100/55 = 55x/55
20 = x
So, the value of x is 20.
