Answer
$\frac{x}{16+2x}$
Work Step by Step
Find the area of the triangle, using A=$\frac{1}{2}$bh. The base is x and the height is x.
$$\frac{(x)(x)}{2} = \frac{x^{2}}{2}$$
Find the area of the rectangle, using A=lw. The length is 8+x and the width is x
$$x\times(8+x)=8x+x^{2}$$
Find the ratio by dividing the area of the triangle by the area of the rectangle. Dividing is equivalent to multiplying by the reciprocal of a number.
$$(\frac{x^{2}}{2})\div(8x+x^{2}) = \frac{x^2}{(2)\times(8x+x^2)} = \frac{x^2}{16x+2x^2} = \frac{x}{16+2x}$$
The length of the rectangle is given by $L = 8+x$
The area of the triangle is given by $A=\frac{1}{2}bh$ or $A=\frac{bh}{2}$
