The length of a rectangle is 4 ft longer than it’s width. If the perimeter of the rectangle is 48 ft, find it’s area
2(w + w+4) = 48
w=10
area = 10*14 ft^2
Let's start by assigning variables to represent the dimensions of the rectangle. Let's say the width of the rectangle is x feet.
According to the problem, the length of the rectangle is 4 feet longer than its width. So, the length will be (x + 4) feet.
The perimeter of a rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 48 feet.
So, we can set up the equation: 2(width) + 2(length) = perimeter.
Plugging in the values we know, the equation becomes: 2(x) + 2(x + 4) = 48.
Simplifying the equation, we get: 2x + 2x + 8 = 48.
Combining like terms, we have: 4x + 8 = 48.
Subtracting 8 from both sides, we get: 4x = 40.
Dividing both sides by 4, we find: x = 10.
Now that we know the width of the rectangle is 10 feet, we can find the length by adding 4 to it: length = 10 + 4 = 14 feet.
Now, let's calculate the area of the rectangle, which is given by the formula: Area = length * width.
Plugging in the values, the area becomes: Area = 10 * 14 = 140 square feet.
So, the area of the rectangle is 140 square feet.
To find the area of the rectangle, we first need to determine the length and width of the rectangle.
Let's denote the width of the rectangle as "w" ft. According to the given information, the length of the rectangle is 4 ft longer than its width, so the length can be expressed as "w + 4" ft.
The perimeter of a rectangle is the sum of the lengths of all its sides, which for a rectangle with length "l" and width "w" would be 2l + 2w. In this case, the perimeter is 48 ft, so we have:
2(l + w) = perimeter
2(w + 4 + w) = 48
Simplifying the equation, we get:
2(2w + 4) = 48
4w + 8 = 48
4w = 40
w = 10
Now that we have the width, we can find the length:
Length = width + 4 = 10 + 4 = 14 ft
Finally, we can calculate the area of the rectangle:
Area = length x width = 14 ft x 10 ft = 140 square feet
Therefore, the area of the rectangle is 140 square feet.