Enter your answer and show all the steps that you use to solve this problem in the space provided. The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are its dimensions?
Let's assume that the width of the rectangle is x cm.
According to the problem, the length of the rectangle is 9.7 cm more than 4 times the width, so the length can be represented as 4x + 9.7 cm.
The perimeter of a rectangle is given by the formula: 2(length + width).
Substituting the length and width from above, the perimeter is:
2(4x + 9.7 +x) = 91.4 cm
Simplifying the equation,
2(5x + 9.7) = 91.4
10x + 19.4 = 91.4
10x = 91.4 - 19.4
10x = 72
x = 72/10
x = 7.2 cm
Now, we can find the length using the width:
Length = 4x + 9.7
Length = 4(7.2) + 9.7
Length = 28.8 + 9.7
Length = 38.5 cm
Therefore, the dimensions of the rectangle are:
Width = 7.2 cm
Length = 38.5 cm
Step 1: Assign variables
Let's assign variables to the dimensions of the rectangle.
Let's say the width of the rectangle is "W" cm.
Therefore, the length of the rectangle is 4W + 9.7 cm.
Step 2: Calculate the perimeter
The perimeter of a rectangle can be calculated by adding the lengths of all the sides.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (length + width)
Using this formula, we can write the equation:
91.4 = 2 * (4W + 9.7 + W)
Step 3: Simplify the equation
Distribute the 2 into the parentheses:
91.4 = 2 * (5W + 9.7)
Multiply 2 by each term inside the parentheses:
91.4 = 10W + 19.4
Subtract 19.4 from both sides of the equation:
91.4 - 19.4 = 10W
72 = 10W
Step 4: Solve for W
Divide both sides of the equation by 10:
72 / 10 = W
7.2 = W
Step 5: Calculate the length of the rectangle
Using the value of W, we can substitute it into the expression we found earlier for the length: 4W + 9.7
4(7.2) + 9.7 = 28.8 + 9.7 = 38.5 cm
Step 6: Determine the dimensions of the rectangle
The width is 7.2 cm and the length is 38.5 cm.