Patrick has just finished building a pen for his new dog. the pen is 3 feet wider than it is long. he also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base. after putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen. he also finds that the perimeter of the pen is 3 times greater than the perimeter of the doghouse. if x represents the length of the pen and y represents the area of the doghouse, then which of the following systems of equations can be used to determine the length and width of the pen and the area of the doghouse?

In the figure below there is a representation of this problem. so, the surface area in green represents the pen and the surface area in black represents the doghouse.  let's solve this problem by expressing the equations according to each statement above, so: 1.  the pen is 3 feet wider than it is long: x: represents the length of the pen  3x:   represents the width  of the pen  2.  he also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base.y: represents the area of the doghouse3.  after putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen.4.  he also finds that the perimeter of the pen is 3 times greater than the perimeter of the doghouse.∴  using these equations you can solve this problem.