The rectangle shown has a perimeter of 118 cm and the given area. Its length is 4 more than four times its width. Write and solve a system of equations to find the dimensions of the rectangle.
(rectangle has an area of 528 cm^2)
The length of the rectangle is ___ cm
The width of the rectangle is ___ cm
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 ABCD is similar to Rectangle WXYZ. The area of ABCD is 30 square inches. Explain how to find the area, x, of WXYZ.
Let's assume the width of the rectangle is "w" cm.
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
To solve this problem, let's assume the width of the rectangle is represented by 'w' 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