If two similar triangles have sides in the ratio a : b, then their areas are in the ratio a² : b².
We have the ratio:
[tex]54:18=\dfrac{54}{18}=3:1[/tex]
Area of the smaler triangle = x
Area of the larger triangle = 567 cm²
Therefore we have the equation:
[tex]567:x=3^2:1^2\\\\\dfrac{567}{x}=\dfrac{9}{1}\qquad|\text{cross multiply}\\\\9x=567\qquad|\text{divide both sides by 9}\\\\x=63[/tex]
Answer: C. 63 cm²
