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? Easily writeable.
Let's assume that the width of the rectangle is x cm.
According to the given information, the length of the rectangle is 9.7 cm more than 4 times the width. So, the length = 4x + 9.7 cm.
Perimeter of a rectangle = 2(length + width)
Given, perimeter = 91.4 cm
2(4x + 9.7 + x) = 91.4
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
So, the width of the rectangle is 7.2 cm.
Substituting the value of x in the length equation, we get:
Length = 4x + 9.7 = 4*7.2 + 9.7 = 28.8 + 9.7 = 38.5 cm.
Hence, the dimensions of the rectangle are width = 7.2 cm and length = 38.5 cm.
To find the dimensions of the rectangle, we can use the information provided and set up equations based on the given conditions.
Let's assume the width of the rectangle is "w" cm.
According to the given conditions, the length of the rectangle is 9.7 cm more than 4 times the width, which can be expressed as 4w + 9.7.
The formula for the perimeter of a rectangle is given by P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width of the rectangle.
In this case, 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)
First, let's simplify the equation:
91.4 = 2(5w + 9.7)
Now, distribute the 2 to the terms inside the parentheses:
91.4 = 10w + 19.4
Next, isolate the variable by subtracting 19.4 from both sides:
91.4 - 19.4 = 10w
72 = 10w
Divide both sides by 10 to solve for w:
w = 7.2
Now, we know that the width of the rectangle is 7.2 cm.
To find the length, we can substitute this value back into the expression for the length:
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.
Let's start by assigning variables to the dimensions of the rectangle. Let's say the width of the rectangle is 'w' cm, and the length is 'l' cm.
According to the given information, the length of the rectangle is 9.7 cm more than 4 times the width. We can write this as follows:
l = 4w + 9.7
The perimeter of the rectangle is the sum of all its sides. In this case, it is given as 91.4 cm. For a rectangle, the perimeter can be calculated using the formula:
Perimeter = 2(l + w)
We can substitute the value of 'l' from the first equation into the perimeter equation and solve for 'w':
91.4 = 2((4w + 9.7) + w)
Now we can simplify the equation:
91.4 = 2(5w + 9.7)
91.4 = 10w + 19.4
91.4 - 19.4 = 10w
72 = 10w
w = 7.2
We have found the value of 'w' to be 7.2 cm.
Now we can substitute this value back into the equation for 'l' to find its value:
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 7.2 cm for the width and 38.5 cm for the length.