The perimeter of a rectangle is 82 feet. Find the length and width of the rectangle if the length is 7 feet more than width.
17ft
Let's let "x" represent the width of the rectangle.
According to the problem, the length of the rectangle is 7 feet more than the width. So, the length is x + 7.
The formula for the perimeter of a rectangle is given by the equation:
Perimeter = 2 * (Length + Width)
In this case, the perimeter is given as 82 feet, so we can rewrite the equation as:
82 = 2 * (x + 7 + x)
Now, let's simplify and solve for x:
82 = 2 * (2x + 7)
82 = 4x + 14
Subtracting 14 from both sides:
82 - 14 = 4x
68 = 4x
Dividing both sides by 4:
68 / 4 = x
x = 17
So, the width of the rectangle is 17 feet.
Now, we can find the length by substituting the value of x back into the equation for the length:
Length = x + 7
Length = 17 + 7
Length = 24
Therefore, the length of the rectangle is 24 feet.
In conclusion, the width of the rectangle is 17 feet and the length is 24 feet.
To find the length and width of the rectangle, we can set up equations based on the given information.
Let's say the width of the rectangle is "w" feet. According to the problem, the length is 7 feet more than the width. So, the length would be "w + 7" feet.
Now, we can use the formula for the perimeter of a rectangle to set up an equation. The perimeter of a rectangle is the sum of all its sides.
Perimeter = 2(length + width)
Since the perimeter of the rectangle is given as 82 feet, we can write the equation as:
82 = 2(w + (w + 7))
Simplifying the equation:
82 = 2(2w + 7)
82 = 4w + 14
4w = 82 - 14
4w = 68
Dividing both sides of the equation by 4:
w = 68/4
w = 17
So, the width of the rectangle is 17 feet.
Now, we can find the length by substituting this value back into our expression for length:
Length = width + 7
Length = 17 + 7
Length = 24
Therefore, the length of the rectangle is 24 feet and the width is 17 feet.
P = 2L + 2W
82 = 2(W + 7) + 2W
82 = 4W + 14
68 = 4W
? = W