Note: 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?
(3 points)
Let's assume 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 would be (4x + 9.7) cm.
The formula for the perimeter of a rectangle is P = 2(length + width). Substituting the values we have:
91.4 = 2((4x + 9.7) + x)
Simplifying further:
91.4 = 2(5x + 9.7)
91.4 = 10x + 19.4
Subtracting 19.4 from both sides:
72 = 10x
Dividing by 10:
7.2 = x
So, the width of the rectangle is 7.2 cm.
Now, plugging this value back into the length equation:
Length = 4x + 9.7
Length = 4(7.2) + 9.7
Length = 28.8 + 9.7
Length = 38.5 cm
Therefore, the width of the rectangle is 7.2 cm and the length is 38.5 cm.
Let's denote the width of the rectangle as "w" and the length of the rectangle as "l".
Step 1: Set up equations based on the given information.
Given: The length of the rectangle is 9.7 cm more than 4 times the width.
l = 4w + 9.7
Given: The perimeter of the rectangle is 91.4 cm.
Perimeter of a rectangle = 2(l + w)
91.4 = 2(l + w)
Step 2: Substitute the value of "l" from the first equation into the second equation.
91.4 = 2((4w + 9.7) + w)
Step 3: Simplify the equation and solve for "w".
91.4 = 2(5w + 9.7)
91.4 = 10w + 19.4
10w = 91.4 - 19.4
10w = 72
w = 72/10
w = 7.2 cm
Step 4: Substitute the value of "w" into the first equation to find the value of "l".
l = 4(7.2) + 9.7
l = 28.8 + 9.7
l = 38.5 cm
Step 5: The dimensions of the rectangle are:
Width = 7.2 cm
Length = 38.5 cm