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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's start by assigning variables to the dimensions of the rectangle. Let's say 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. Therefore, the length of the rectangle can be represented by the expression 4W + 9.7 cm.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 (length + width)
In this case, the perimeter is given as 91.4 cm. So we can set up the equation:
91.4 cm = 2 (4W + 9.7 cm + W)
Now let's solve for W:
91.4 cm = 2 (5W + 9.7 cm)
Divide by 2 to isolate the expression:
45.7 cm = 5W + 9.7 cm
Subtract 9.7 cm from both sides:
36 cm = 5W
Divide both sides by 5:
W = 7.2 cm
Now that we have found the width, we can substitute this value back into the expression we found for the length:
Length = 4W + 9.7 cm
= 4(7.2 cm) + 9.7 cm
= 28.8 cm + 9.7 cm
= 38.5 cm
Therefore, the dimensions of the rectangle are:
Width = 7.2 cm
Length = 38.5 cm
Let's call the width of the rectangle "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 for the length as:
Length = 4w + 9.7
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
Substituting the given values, we can write the equation for the perimeter as:
91.4 = 2 * (4w + 9.7 + w)
Simplifying the equation:
91.4 = 2 * (5w + 9.7)
91.4 = 10w + 19.4
91.4 - 19.4 = 10w
72 = 10w
Dividing both sides by 10:
7.2 = w
So, the width of the rectangle is 7.2 cm.
To find the length, we can substitute this value back into the equation for the length:
Length = 4w + 9.7
Length = 4(7.2) + 9.7
Length = 28.8 + 9.7
Length = 38.5
Therefore, the length of the rectangle is 38.5 cm.
The dimensions of the rectangle are 7.2 cm (width) and 38.5 cm (length).
To find the dimensions of the rectangle, we can start by setting up equations using 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. Therefore, the length can be represented as (4w + 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.
Plugging in the given perimeter value of 91.4 cm, we can write the equation as:
91.4 = 2((4w + 9.7) + w)
Now, let's solve the equation step by step:
1. Distribute the 2 to terms within the parentheses:
91.4 = 2(4w + 9.7 + w)
91.4 = 2(5w + 9.7)
2. Apply the distributive property:
91.4 = 10w + 19.4
3. Subtract 19.4 from both sides of the equation:
91.4 - 19.4 = 10w + 19.4 - 19.4
72 = 10w
4. Divide both sides of the equation by 10:
72 / 10 = 10w / 10
7.2 = w
Now that we have the value for the width, we can substitute it back into any of our previous equations to find the length.
Using the equation for the length, we have:
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