The length of a rectangle is 12 in. and the perimeter is 56 in. Find the width of the rectangle.
A) 22 in.
B) 21 in.
C) 32 in.
D) 16 in.
Answer (1)
We have a rectangle with length l = 12 inches and perimeter P = 56 inches.
The perimeter formula is P = 2 l + 2 w , where w is the width.
Substitute the given values: 56 = 2 ( 12 ) + 2 w , which simplifies to 56 = 24 + 2 w .
Solving for w , we get w = 2 56 − 24 = 2 32 = 16 .
The width of the rectangle is 16 in.
Explanation
Problem Analysis We are given the length and the perimeter of a rectangle and asked to find its width. Let's denote the length by l and the width by w . We know that l = 12 inches and the perimeter P = 56 inches.
Perimeter Formula The formula for the perimeter of a rectangle is given by: P = 2 l + 2 w
Substitution We can substitute the given values into the formula: 56 = 2 ( 12 ) + 2 w
Solve for width Now, we solve for w :
56 = 24 + 2 w
Isolate the term with width Subtract 24 from both sides of the equation: 56 − 24 = 2 w 32 = 2 w
Calculate the width Divide both sides by 2 to find the width: 2 32 = w w = 16
Final Answer Therefore, the width of the rectangle is 16 inches. The correct answer is D) 16 in.
Examples
Understanding how to calculate the dimensions of a rectangle is useful in many real-world scenarios. For example, if you're building a rectangular garden and have a specific amount of fencing (perimeter) and a desired length, you can calculate the required width to maximize the garden's area. This ensures you use your resources efficiently and create the garden you envision. Similarly, interior designers use these calculations to arrange furniture in a room, ensuring a balanced and aesthetically pleasing layout.
