if w is the width, the length must be 4w+4
So, you need to solve
2(w + 4w+4) = 118
5w+4 = 59
w = 11
so the length is 48
(rectangle has an area of 528 cm^2)
The length of the rectangle is ___ cm
The width of the rectangle is ___ cm
So, you need to solve
2(w + 4w+4) = 118
5w+4 = 59
w = 11
so the length is 48
According to the problem, the length of the rectangle is 4 more than four times its width. So, the length of the rectangle is (4w+4) cm.
To find the dimensions of the rectangle, we can set up a system of equations.
First equation: Perimeter of the rectangle is 118 cm.
Perimeter of a rectangle = 2 * (Length + Width)
118 = 2(4w + 4 + w)
Simplifying the equation, we get:
118 = 10w + 8
Second equation: Area of the rectangle is 528 cm².
Area of a rectangle = Length * Width
528 = (4w + 4) * w
Now, we can solve this system of equations to find the width and length of the rectangle.
Let's solve the first equation for w:
118 = 10w + 8
10w = 118 - 8
10w = 110
w = 110/10
w = 11 cm
Now, substitute the value of w into the second equation and solve for the length:
528 = (4w + 4) * w
528 = (4 * 11 + 4) * 11
528 = (44 + 4) * 11
528 = 48 * 11
528 = 528
Therefore, the width of the rectangle is 11 cm and the length of the rectangle is (4 * 11 + 4) cm = 48 cm.
So, the dimensions of the rectangle are:
Width: 11 cm
Length: 48 cm
According to the problem, the length of the rectangle is 4 more than four times its width. So, the length can be represented as 4w + 4 cm.
We are given that the perimeter of the rectangle is 118 cm. The formula for the perimeter of a rectangle is given by 2(length + width).
Using this information, we can write the first equation:
2(4w + 4 + w) = 118
Simplifying this equation, we get:
10w + 8 = 118
Subtracting 8 from both sides:
10w = 110
Dividing both sides by 10:
w = 11
So, the width of the rectangle is 11 cm.
Now, let's find the length using the second equation. The length is given as 4 more than four times the width:
Length = 4w + 4
Substituting the value of w, we get:
Length = 4(11) + 4
Length = 44 + 4
Length = 48
So, the length of the rectangle is 48 cm.
Therefore, the dimensions of the rectangle are:
Width = 11 cm
Length = 48 cm