The perimeter of a rectangular field is 280 feet. The perimeter of a larger rectangular field is 3 times as long as the smaller field. If the length of the larger field is 250 feet, what is its width in feet?
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We have a problem about rectangular fields and their perimeters. The smaller field has a perimeter of 280 feet. The larger field has a perimeter that is 3 times longer than the smaller field. We know the length of the larger field is 250 feet, and we need to find its width.
Let's solve this step by step. First, we need to calculate the perimeter of the larger field. We know the smaller field has a perimeter of 280 feet, and the larger field's perimeter is 3 times as long. So we multiply 280 by 3 to get 840 feet for the larger field's perimeter.
Now we apply the rectangle perimeter formula. The perimeter of a rectangle equals 2 times the sum of length and width. For our larger field, we substitute the known values: 840 equals 2 times the quantity 250 plus the unknown width. This gives us the equation we need to solve.
Now let's solve the equation step by step. We start with 840 equals 2 times the quantity 250 plus width. First, we divide both sides by 2, which gives us 420 equals 250 plus width. Then we subtract 250 from both sides to isolate the width. This gives us 170 equals width. So the width of the larger field is 170 feet.