The length of a rectangle is 12 in. and the perimeter is 56 in. Find the width of the rectangle.
A) 16 in.
B) 32 in.
C) 22 in.
Answer (1)
Substitute the given length and perimeter into the formula for the perimeter of a rectangle: 56 = 2 ( 12 ) + 2 w .
Simplify the equation: 56 = 24 + 2 w .
Isolate the term with the width: 32 = 2 w .
Solve for the width: w = 16 . The width of the rectangle is 16 in.
Explanation
Problem Analysis Let's analyze the problem. We are given the length and perimeter of a rectangle and need to find its width. We know that the perimeter of a rectangle is given by the formula P = 2 l + 2 w , where l is the length and w is the width. We are given l = 12 inches and P = 56 inches. We need to solve for w .
Substitute Values Now, let's substitute the given values into the perimeter formula: 56 = 2 ( 12 ) + 2 w
Simplify Simplify the equation: 56 = 24 + 2 w
Isolate the term with width Subtract 24 from both sides of the equation: 56 − 24 = 2 w 32 = 2 w
Solve for width Divide both sides by 2 to solve for w :
2 32 = w 16 = w
Final Answer Therefore, the width of the rectangle is 16 inches.
Examples
Understanding the dimensions of rectangles is crucial in many real-world applications. For example, when designing a rectangular garden, knowing the length and perimeter helps determine the width and the amount of fencing needed. Similarly, in construction, calculating the dimensions of rooms or buildings requires a solid grasp of rectangular geometry. This problem demonstrates a fundamental concept used in various fields, from landscaping to architecture.
