Answer
See explanation
Work Step by Step
Using the formula for the perimeter of a rectangle:
$$P=2(x+y)$$
Substituting $P=\frac{1040}{3}$:
$$\frac{1040}{3}=2(x+y)$$
Simplifying:
$$\frac{\frac{1040}{3}}{2}=x+y$$
$$\frac{520}{3}=x+y$$
$$\frac{520}{3}-x=y$$
Then,
$$y=\frac{520}{3}-x$$
Using the formula for the area of a rectangle:
$$A=xy$$
Substituting $y=\frac{520}{3}-x$, then:
$$A=x\left(\frac{520}{3}-x\right)$$
