Answer :
Think of it like this. The perimeter is 72 feet. The length, l, is 18 feet longer than the width, w. So, l=w+18.
Perimeter is calculated by adding the lengths of all four sides together, AKA adding the length twice and the width twice: l+w+l+w.
Since l=w+18, we can substitute this in for l in the expression above: l+w+l+w=w+18+w+w+18+w
Simplified, we combine like terms, the w's and the 18's: 4w+36. This is the perimeter.
The perimeter is 72 feet, so 72=4w+36. To find the width, we need to isolate w. First, subtract 36 from both sides: 72-36=4w+36-36. Simplified: 36=4w. Then, divide 4 on both sides to get w alone. 36/4=4w/4. w=9. Therefore, the width of the rectangle is 9 feet.
Since the length of the rectangle is w+18, and w=9, we know that l=9+18=27. So w=9, and l=27. The length is 27 feet.
In a rectangle, we find area by multiplying length by width: A=lw. To find the area of the yard, multiply 27 by 9: A=27*9=243. Since 27 and 9 are both measurements in feet, the answer is 243 square feet.
Answer: The area of the yard is 243 square feet.
Perimeter is calculated by adding the lengths of all four sides together, AKA adding the length twice and the width twice: l+w+l+w.
Since l=w+18, we can substitute this in for l in the expression above: l+w+l+w=w+18+w+w+18+w
Simplified, we combine like terms, the w's and the 18's: 4w+36. This is the perimeter.
The perimeter is 72 feet, so 72=4w+36. To find the width, we need to isolate w. First, subtract 36 from both sides: 72-36=4w+36-36. Simplified: 36=4w. Then, divide 4 on both sides to get w alone. 36/4=4w/4. w=9. Therefore, the width of the rectangle is 9 feet.
Since the length of the rectangle is w+18, and w=9, we know that l=9+18=27. So w=9, and l=27. The length is 27 feet.
In a rectangle, we find area by multiplying length by width: A=lw. To find the area of the yard, multiply 27 by 9: A=27*9=243. Since 27 and 9 are both measurements in feet, the answer is 243 square feet.
Answer: The area of the yard is 243 square feet.