The length of a rectangle is 6 inches more than the width. If the perimeter is 176 inches, what are the length and the width?
2(w + w+6) = 176
To solve this problem, we can set up two equations based on the given information.
Let's assume that the width of the rectangle is represented by the variable 'w', and the length is represented by the variable 'l'.
From the given information, we know that the length (l) is 6 inches more than the width (w). So, we can write the equation:
l = w + 6 -- Equation 1
The perimeter of a rectangle is calculated by adding the lengths of all sides. For a rectangle, the formula for perimeter is 2(l + w). So, we can write the second equation:
2(l + w) = 176 -- Equation 2
Now, we have a system of two equations with two variables. We can solve this system to find the values of 'l' and 'w'.
Step 1: Substitute the value of 'l' from Equation 1 into Equation 2.
2((w + 6) + w) = 176
Simplify:
2(2w + 6) = 176
Step 2: Simplify further.
4w + 12 = 176
Step 3: Subtract 12 from both sides of the equation.
4w = 164
Step 4: Divide both sides of the equation by 4.
w = 41
Now that we know the width (w = 41), we can substitute this value back into Equation 1 to find the length (l).
l = w + 6 = 41 + 6 = 47
Therefore, the width of the rectangle is 41 inches, and the length of the rectangle is 47 inches.