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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 the width of the rectangle be w.
According to the problem, the length of the rectangle is 9.7 cm more than 4 times the width, which can be expressed as 4w + 9.7.
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, the perimeter is given as 91.4 cm. Therefore, we can set up the equation:
2(width) + 2(length) = perimeter
2w + 2(4w + 9.7) = 91.4
Simplifying the equation, we get:
2w + 8w + 19.4 = 91.4
10w + 19.4 = 91.4
Subtracting 19.4 from both sides gives:
10w = 72
Dividing both sides by 10 gives:
w = 7.2
So, the width of the rectangle is 7.2 cm.
Plugging this value back into the expression for the length, we get:
length = 4w + 9.7
length = 4(7.2) + 9.7
length = 28.8 + 9.7
length = 38.5
Therefore, the dimensions of the rectangle are 7.2 cm by 38.5 cm.
Let's assume the width of the rectangle is "w" cm.
The length of the rectangle is given as 9.7 cm more than 4 times the width, which can be expressed as 4w + 9.7 cm.
The perimeter of a rectangle is calculated by adding all four sides:
Perimeter = 2 * (length + width)
We are given that the perimeter of the rectangle is 91.4 cm, so we can set up the equation:
91.4 = 2 * (4w + 9.7 + w)
Now let's solve this equation step-by-step:
1. Distribute the 2 to each term inside the parentheses:
91.4 = 2 * 4w + 2 * 9.7 + 2 * w
91.4 = 8w + 19.4 + 2w
2. Combine like terms:
91.4 = 10w + 19.4
3. Subtract 19.4 from both sides to isolate the variable:
91.4 - 19.4 = 10w + 19.4 - 19.4
72 = 10w
4. Divide both sides by 10 to solve for "w":
(72) / 10 = (10w) / 10
7.2 = w
Therefore, the width of the rectangle is 7.2 cm.
To find the length of the rectangle, substitute the value of "w" into the expression for 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
Length = 38.5 cm
To solve this problem, we need to set up an equation based on the given information and then solve for the dimensions of the rectangle. Let's denote the width of the rectangle as "w" and the length as "l".
From the problem, we know that the length of the rectangle is 9.7 cm more than 4 times the width. This can be expressed as:
l = 4w + 9.7
We are also given that the perimeter of the rectangle is 91.4 cm. The perimeter of a rectangle is calculated by adding the lengths of all sides. In this case, it would be expressed as:
perimeter = 2(l + w)
Now we can substitute the value of l from the first equation into the second equation:
91.4 = 2((4w + 9.7) + w)
Simplifying the equation:
91.4 = 2(5w + 9.7)
91.4 = 10w + 19.4
Next, we need to isolate the variable "w". Let's subtract 19.4 from both sides of the equation:
91.4 - 19.4 = 10w
72 = 10w
To solve for "w", we divide both sides of the equation by 10:
w = 72/10
w = 7.2
Now that we have the value of "w", we can substitute it back into the first equation to find the length "l":
l = 4w + 9.7
l = 4(7.2) + 9.7
l = 28.8 + 9.7
l = 38.5
Therefore, the dimensions of the rectangle are width = 7.2 cm and length = 38.5 cm.