Perimeter of a rectangular

Question

The perimeter of a rectangular field is 360 yd. The length is 40 yd longer than the width. Find the dimensions.

Answer 1

The perimeter of any polygon is the sum of the exterior sides of that polygon.

 

Assign variables for the dimensions.

 

Let width = x

Let length = x + 40

Perimeter = 360 yds

 

Set up an equation based on the situation. The perimeter of a rectangle is

 

2(length) + 2(width) = Perimeter

 

so

 

2x + 2(x + 40) = 360

 

Solve for x.

 

 

2x + 2x + 80 = 360

 

4x + 80 = 360

 

4x = 280

  x = 70

 

 

Substitute this value of x into the dimensions.

 

width = 70 yds

length = 110 yds

Answer 2

Justin, this is easier than it seems, I promise.

 

We know that the perimeter is 2l + 2w.  Since the length is 40 yards longer than the width, it is equal to w + 40.

 

So, we now have 2(w + 40) + 2w = 360

 

Distributing, we get 2w + 80 + 2w = 360

 

Combining like terms, we get 4w + 80 = 360

 

Subtracting 80 from both sides, we get 4w = 280

 

Dividing both sides by 4, we get w = 70

 

The length is 40 yards longer, so 70 + 40 = 110

 

Let's check. 2(70) + 2(110) = 140 + 120 = 360.  Check!