Answer
The dimensions of the rectangle are 100 m x 50 m. If the length is 100m, the width is 50m. If the length is 50m, the width is 100m.
Work Step by Step
The perimeter is 300 meters and is represented by 2x+2y.
The area is 5000 square meters and is represented by xy.
$$2x+2y=300$$
$$xy=5000$$
$$x=\frac{5000}{y}$$
$$2(\frac{5000}{y})+2y=300$$
$$\frac{10000}{y}+2y=300$$
$$10000+2y^2=300y$$
$$2y^2-300y+10000=0$$
$$y^2-150y+5000=0$$
$$(y-100)(y-50)=0$$
$$y=100,50$$
$$xy=5000$$
$$100x=5000$$
$$x=50$$
$$xy=5000$$
$$50x=5000$$
$$x=100$$
The dimensions of the rectangle are 100 m x 50 m. If the length is 100m, the width is 50m. If the length is 50m, the width is 100m.