The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. What are the dimensions of the rectangle?
Width = W.
Length = W+1 cm.
2W + 2(W+1) = 34.
W = ?
W+1 = ?
L = Length
W = Width
The length is 1 cm longer than the width means:
L = W + 1
The perimeter of a rectangle:
P = 2 W + 2 L
P = 2 ( L + W )
Replace P = 34 and L = W + 1 in this equation
34 = 2 ( W + 1 + W )
34 = 2 ( 2 W +1 )
Divide both sides by 2
17 = 2 W + 1
Subtract1 to both sides
16 = 2 W
2 W = 16
Divide both sides by 2
W = 8 cm
L = W + 1 = 8 + 1 = 9 cm
P = 2 ( L + W )
P = 2 * ( 9 + 8 )
P = 2 * 17 = 34 cm
w=8 ? w+1=9? @henry2
To solve this problem, we can set up two equations based on the information given:
1) Perimeter of a rectangle = 2 * (Length + Width)
2) Length = Width + 1
Let's use these equations to find the dimensions of the rectangle.
1) Substituting the second equation into the first equation, we get:
34 cm = 2 * (Width + (Width + 1))
2) Simplifying the equation:
34 cm = 2 * (2 * Width + 1)
34 cm = 4 * Width + 2
3) Subtracting 2 from both sides of the equation:
34 cm - 2 = 4 * Width
32 cm = 4 * Width
4) Dividing both sides of the equation by 4:
8 cm = Width
5) Substituting the value of Width into the second equation to find the length:
Length = Width + 1
Length = 8 cm + 1
Length = 9 cm
Therefore, the dimensions of the rectangle are a width of 8 cm and a length of 9 cm.