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The area of a triangle is $3$ times less than $2$ times the area of a rectangle. If the sum of the two areas is $64$ square meters, what is the area of the triangle and what is the area of the rectangle?

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Hint: Let the area of the triangle be $T$, and the area of the rectangle be $R$. The information given implies:

  • $T = 2 R / 3$
  • $T + R = 64$
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Because $T=\frac{2R}{3}$ and $T+R=64$, we have that $\frac{2R}{3}+R=64$ and $\frac{5R}{3}=64$ and $5R=192$. Therefore, $R=38.4$ square meters and $T=\frac{2*38.4}{3}$ = $25.2$ square meters.

The area of the triangle is $25.2$ square meters and the area of the rectangle is $38.4$ square meters.

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