Note: Enter your answer and show all the steps that you use to solve this problem.
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 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 is (4x + 9.7) cm.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
For this problem, we have:
91.4 = 2((4x + 9.7) + x) cm
Simplifying the equation:
91.4 = 2(5x + 9.7) cm
91.4 = 10x + 19.4 cm
91.4 - 19.4 = 10x cm
72 = 10x cm
x = 7.2 cm
Now, we have the width of the rectangle, which is 7.2 cm.
Substituting the value of x back into the equation for the length, we get:
Length = 4x + 9.7 cm
Length = 4(7.2) + 9.7 cm
Length = 28.8 + 9.7 cm
Length = 38.5 cm
Therefore, the dimensions of the rectangle are:
Width = 7.2 cm
Length = 38.5 cm
Let's start by assigning variables to the dimensions of the rectangle.
Let:
Length = L
Width = W
According to the problem, the length of the rectangle is 9.7 cm more than 4 times the width, so we can write the equation:
L = 4W + 9.7 .....(1)
The perimeter of a rectangle is given by the formula:
Perimeter = 2(L + W)
Substituting the values from equation (1) into the formula for perimeter, we get:
91.4 = 2(4W + 9.7 + W)
Simplifying the equation:
91.4 = 2(5W + 9.7)
91.4 = 10W + 19.4
Subtracting 19.4 from both sides:
91.4 - 19.4 = 10W
72 = 10W
Dividing both sides by 10:
W = 7.2
Now, substitute the value of W back into equation (1) to find the value of L:
L = 4(7.2) + 9.7
L = 28.8 + 9.7
L = 38.5
Therefore, the dimensions of the rectangle are:
Length = 38.5 cm
Width = 7.2 cm
To find the dimensions of the rectangle, we can first set up equations based on the given information. Let's assume the width of the rectangle is "w" 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 (4w + 9.7) cm.
The perimeter of the rectangle is the sum of all four sides, which is given as 91.4 cm. The formula for the perimeter of a rectangle is P = 2*(length + width).
Setting up the equation using the given information:
91.4 = 2 * ((4w + 9.7) + w)
Simplifying the equation:
91.4 = 2 * (5w + 9.7)
Divide both sides by 2:
45.7 = 5w + 9.7
Subtracting 9.7 from both sides:
36 = 5w
Divide both sides by 5:
w = 7.2 cm
Now that we have the width, we can substitute this value into the expression for the length:
Length = 4w + 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 and length = 38.5 cm.