solve arithmetically and algebraically.
The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
In mathematics, we commonly use the following formula for perimeter of a rectangle: P = 2L + 2W so 54=2(6)+2(x)
54=12+2(21)
W=21cm
Usually the length is longer than the width. Double check your answer and problem
To solve this problem, we can use both arithmetic and algebra.
Arithmetically:
We know that the perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 54 cm.
Since a rectangle has two pairs of equal sides, we can split the perimeter into two equal parts: length + width + length + width.
Given that the length is 6 cm, we can rewrite the perimeter equation as:
2(6 cm + width) = 54 cm.
Simplifying the equation:
12 cm + 2width = 54 cm.
Subtracting 12 cm from both sides:
2width = 42 cm.
Finally, dividing both sides by 2:
width = 21 cm.
Therefore, arithmetically, the width of the rectangle is 21 cm.
Algebraically:
We can also solve this problem algebraically using a variable. Let's assume the width of the rectangle is represented by 'w'.
The perimeter of the rectangle is given as 54 cm, so we can write the equation as:
2(6 cm + w) = 54 cm.
Expanding and simplifying the equation:
12 cm + 2w = 54 cm.
Subtracting 12 cm from both sides:
2w = 42 cm.
Finally, dividing both sides by 2:
w = 21 cm.
Therefore, algebraically, the width of the rectangle is 21 cm, which matches the arithmetical solution.