Solve each problem algebraically using two variables.
The perimeter of a rectangle is 50 centimeters. The length is 9 centimeters more than the width. Find the length and the width of the rectangle
L = W + 9
2L + 2W = 2(W+9) + 2W = 50
Solve for W, then L.
P= 50
L= W + 9
P=2L + 2W
P= 2*(W +9) +2W
50 = 2W+18+2W
4W = 50-18
4W = 32
W = 8
L = W+9
L = 8 + 9
L = 17
therefore, L= 17 and w =8
not sure if my work is correct
Let's assume the width of the rectangle is x centimeters.
According to the problem, the length is 9 centimeters more than the width. So the length is x + 9 centimeters.
The perimeter of a rectangle is the sum of all its sides.
Since a rectangle has two pairs of equal sides (length and width), the perimeter can be calculated as:
Perimeter = 2 * (Length + Width)
Substituting the given values, we get:
50 = 2 * (x + (x + 9))
Simplifying the equation:
50 = 2 * (2x + 9)
50 = 4x + 18
Now, let's isolate the variable:
4x = 50 - 18
4x = 32
x = 32/4
x = 8
So the width of the rectangle is 8 centimeters.
Now we can find the length by substituting the value of x:
Length = x + 9 = 8 + 9 = 17
So the length of the rectangle is 17 centimeters.
To solve this problem algebraically using two variables, let's represent the width of the rectangle by the variable 'w' and the length by the variable 'l'.
We know that the perimeter of a rectangle is the sum of all its sides. For a rectangle with length 'l' and width 'w', the formula for the perimeter is:
Perimeter = 2 * (length + width)
In this case, the perimeter is given as 50 centimeters, so we can write the equation as:
50 = 2 * (l + w)
We are also given that the length is 9 centimeters more than the width. In terms of variables, this can be written as:
l = w + 9
Now, we have a system of two equations:
50 = 2 * (l + w)
l = w + 9
To solve this system of equations, we can use the substitution method or the elimination method.
Let's use the substitution method. We'll start by substituting the second equation into the first equation:
50 = 2 * ((w + 9) + w)
Simplifying the equation, we get:
50 = 2 * (2w + 9)
Expanding and simplifying further:
50 = 4w + 18
Now, isolate the variable 'w' by subtracting 18 from both sides:
50 - 18 = 4w
32 = 4w
Divide both sides by 4:
32/4 = w
8 = w
So, the width of the rectangle is 8 centimeters.
Now that we have the value of 'w', we can substitute it back into the second equation to find the length:
l = w + 9
l = 8 + 9
l = 17
Hence, the length of the rectangle is 17 centimeters.
Therefore, the length of the rectangle is 17 cm, and the width of the rectangle is 8 cm.