Answer:
x = 9
Step-by-step explanation:
Similar Triangles
We are given a shape where two similar triangles are given. The similarity theorem states that the side lengths of the triangles must be proportional in the same scale factor.
The total length of the left side is 72+9 = 81 cm
The smaller length of the left side is 9 cm
The proportion is 81/9 = 9. This is the scale factor.
The total length of the right side is 3x - 20 + 56 = 3x + 36
The smaller length of the right side is 3x-20
The proportion must be equal to 9:
[tex]\displaystyle \frac{3x+36}{3x-20}=9[/tex]
Multiplying by 3x-20:
3x+36=9(3x-20)
Operating
3x+36=27x-180
Rearranging:
24x = 216
Dividing by 24:
x = 9
