Similar triangles may or may not be congruent.
The values of a and b are 6 and 22.5, respectively.
Because the triangles are similar, then the following equivalent ratios are true.
[tex]\mathbf{10 : 4 = b : 9 = 15 : a}[/tex]
First, we calculate b using:
[tex]\mathbf{10 : 4 = b : 9}[/tex]
Express as fraction
[tex]\mathbf{\frac{10 }{ 4} = \frac{b } 9}[/tex]
[tex]\mathbf{2.5 = \frac{b } 9}[/tex]
Multiply both sides by 9
[tex]\mathbf{b = 2.5 \times 9}[/tex]
[tex]\mathbf{b = 22.5}[/tex]
Next, we calculate a using:
[tex]\mathbf{10 : 4 = 15 : a}[/tex]
Express as fractions
[tex]\mathbf{\frac{4}{10} = \frac{a}{15}}[/tex]
Multiply both sides by 15
[tex]\mathbf{a= 15 \times \frac{4}{10}}[/tex]
[tex]\mathbf{a= 6}[/tex]
Hence, the values of a and b are 6 and 22.5, respectively.
Read more about similar triangles at:
https://brainly.com/question/20502441
