Select the correct answer.
The perimeter of a rectangle is 42 inches. If the width of the rectangle is 6 inches, what is the length?
A. 12 inches
B. 15 inches
C. 21 inches
D. 40 inches
Answer (2)
Substitute the given perimeter and width into the formula: 42 = 2 l + 2 ( 6 ) .
Simplify the equation: 42 = 2 l + 12 .
Subtract 12 from both sides: 30 = 2 l .
Divide by 2 to find the length: l = 15 inches.
Explanation
Problem Analysis Let's analyze the problem. We are given the perimeter of a rectangle and its width, and we need to find its length. The formula for the perimeter of a rectangle is P = 2 l + 2 w , where P is the perimeter, l is the length, and w is the width. We can substitute the given values into the formula and solve for the length.
Substitute Values We are given that the perimeter P = 42 inches and the width w = 6 inches. Substitute these values into the formula P = 2 l + 2 w :
42 = 2 l + 2 ( 6 ) 42 = 2 l + 12
Isolate the Length Term Now, we need to isolate l . Subtract 12 from both sides of the equation: 42 − 12 = 2 l + 12 − 12 30 = 2 l
Solve for Length Divide both sides by 2 to solve for l :
2 30 = 2 2 l 15 = l
Final Answer So, the length of the rectangle is 15 inches. The correct answer is B.
Examples
Understanding the perimeter of a rectangle is useful in many real-life situations. For example, if you're building a rectangular fence around a garden, you need to know the perimeter to determine how much fencing material to buy. If your garden is 6 feet wide and you want the perimeter to be 42 feet, you can use the formula P = 2 l + 2 w to calculate the required length of the garden. In this case, you would need a length of 15 feet.
The length of the rectangle is 15 inches. This is determined by applying the perimeter formula for a rectangle. The answer is option B.
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