The perimeter of a rectangular field is 372 yards. If the width of the field is 87 yards, what is its length?
Answer (2)
The perimeter of a rectangle is given by P = 2 l + 2 w , where l is the length and w is the width.
Substitute the given values P = 372 and w = 87 into the formula: 372 = 2 l + 2 ( 87 ) .
Solve for l : 372 = 2 l + 174 ⇒ 2 l = 198 ⇒ l = 99 .
The length of the rectangular field is 99 yards.
Explanation
Problem Analysis We are given the perimeter of a rectangular field is 372 yards and the width is 87 yards. We need to find the length of the field.
Perimeter Formula The formula for the perimeter P of a rectangle is given by: P = 2 l + 2 w where l is the length and w is the width.
Substitution We are given P = 372 yards and w = 87 yards. Substituting these values into the formula, we get: 372 = 2 l + 2 ( 87 ) 372 = 2 l + 174
Isolate the term with length To solve for l , we first subtract 174 from both sides of the equation: 372 − 174 = 2 l 198 = 2 l
Solve for length Now, we divide both sides by 2 to find the length: l = 2 198 l = 99
Final Answer Therefore, the length of the rectangular field is 99 yards.
Examples
Understanding how to calculate the dimensions of a rectangle given its perimeter is useful in many real-world scenarios. For example, if you're planning to build a fence around a garden and you know the total length of fencing you have (the perimeter) and the width of the garden, you can calculate the length to maximize the garden's area. This ensures you use your resources efficiently and create the garden you desire. Let's say you have 100 feet of fencing and want the garden to be 20 feet wide. You can use the perimeter formula to find the length: 100 = 2 l + 2 ( 20 ) , which simplifies to l = 30 feet.
The length of the rectangular field can be found using the perimeter formula, which gives us a length of 99 yards when we know the width is 87 yards and the perimeter is 372 yards.
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