On a rectangular sheet of paper, Aiko drew a triangle whose base length is the same as the length of the sheet and whose height is the same as the width of the sheet. What is the ratio of the area of the triangle to the area of the rectangular sheet of paper?

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The area formula for a triangle comes from the fact that it is always a half of its corresponding quadrilateral with same base and height.

$$ A = \frac{1}{2}bh $$ $$ A_{\text{triangle}} = \frac{1}{2}bh $$ $$ A_{\text{rectangle}} = lw $$

The ratio of the area of the triangle to rectangle:

$$ \frac{A_{\text{triangle}}}{A_{\text{rectangle}}} = \frac{\frac{1}{2}bh}{lw} $$

The question mentions \( b=l, h=w \)

$$ \frac{A_{\text{triangle}}}{A_{\text{rectangle}}} = \frac{\frac{1}{2}bh}{bh} $$ $$ \frac{A_{\text{triangle}}}{A_{\text{rectangle}}}= \boxed{\frac{1}{2}} $$