The perimeter of a rectangle is 106 inches,the length exceeds the width by 7 inches, find the length and the width
Let's assume the width of the rectangle is x inches.
Since the length exceeds the width by 7 inches, the length would be (x + 7) inches.
The perimeter of a rectangle can be calculated by the formula:
Perimeter = 2 * (length + width)
According to the given information, the perimeter is 106 inches. So we can write the equation as:
106 = 2 * ((x + 7) + x)
Simplifying the equation:
106 = 2 * (2x + 7)
106 = 4x + 14
4x = 106 - 14
4x = 92
x = 92 / 4
x = 23
Therefore, the width of the rectangle is 23 inches.
To find the length, substitute the value of x back into the equation:
Length = x + 7 = 23 + 7 = 30 inches
So, the length of the rectangle is 30 inches and the width is 23 inches.
To find the length and width of the rectangle, we can set up a system of equations based on the given information. Let's assign variables to represent the length and width:
Let's say the width of the rectangle is "w" inches.
Since the length exceeds the width by 7 inches, the length of the rectangle would be "w + 7" inches.
Now, let's use the information that the perimeter of the rectangle is 106 inches. The formula to calculate the perimeter of a rectangle is P = 2w + 2l, where P is the perimeter, w is the width, and l is the length:
So, we have:
2w + 2(w + 7) = 106
Now, let's solve this equation to find the values of w and (w + 7):
2w + 2w + 14 = 106
4w + 14 = 106
4w = 106 - 14
4w = 92
w = 92 / 4
w = 23
So, the width of the rectangle is 23 inches.
To find the length, we can substitute the value of w back into the expression (w + 7):
l = w + 7
l = 23 + 7
l = 30
Therefore, the length of the rectangle is 30 inches, and the width is 23 inches.
2l + 2w=106
2(w+7)+2w=106
you take it from here.
the answers are...
w=23
l=30
use this formula...
2L+2W=106
2(w+7)+2W=106
^Factor the 2 with (W+7)
then solve for W.
thats the first part.
then use the same formula...
2L+2W=106
plug in your W
then solve for L