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Two corresponding sides of two similar triangles are 3cm and 5cm. The area of the first triangle is 12cm^2. What is the area of the second triangle?
Since the triangles are similar, their corresponding sides are proportional. In this case the proportion is 3:5. However, the area is calculate by multiplying 2 sides or a side and an altitude. This means the area is squarely proportional to the sides. The area of the second triangle would be \[\left( \frac{ 3 }{ 5 } \right)^{2}\] multiplied by the area of the first triangle.
Oops, I meant \[\left( \frac{ 5 }{ 3 } \right)^{2}\]