a rectangle with a perimeter of 54cm is 3cm longer than it is wide. what are its length and width?
P = 2L + 2W
54 = 2(W + 3) + 2W
To find the length and width of a rectangle, given its perimeter and the information that it is 3cm longer than it is wide, we can follow these steps:
Step 1: Let's represent the width of the rectangle as "x" cm.
Step 2: According to the problem, the length of the rectangle is 3 cm longer than its width, so the length can be represented as "x + 3" cm.
Step 3: The formula for the perimeter of a rectangle is: P = 2(length + width). Substituting the values we have:
54 cm = 2(x + (x + 3)).
Step 4: Simplify the equation:
54 cm = 2(2x + 3).
54 cm = 4x + 6.
Step 5: Solve for "x":
54 cm - 6 = 4x.
48 cm = 4x.
x = 12 cm.
Step 6: Now that we know the width (x = 12 cm), we can find the length:
Length = Width + 3.
Length = 12 cm + 3 cm.
Length = 15 cm.
Therefore, the length of the rectangle is 15 cm and the width is 12 cm.
To find the length and width of the rectangle, we need to set up equations based on the given information.
Let's assume the width of the rectangle is "x" cm. Since the rectangle is 3 cm longer than it is wide, the length of the rectangle would be "x + 3" cm.
The perimeter of a rectangle is the sum of all its sides. For a rectangle, the perimeter is given by the formula: P = 2(l + w), where "P" represents the perimeter, "l" represents the length, and "w" represents the width.
From the given information, we know that the perimeter is 54 cm. Plugging in the values into the formula, we have:
54 = 2(x + x + 3)
Now, we can simplify and solve for "x":
54 = 2(2x + 3)
54 = 4x + 6
48 = 4x
x = 12
Therefore, the width of the rectangle is 12 cm, and the length would be 12 + 3 = 15 cm.