The yard behind the cindy’s house is rectangular in shape and has a perimeter of 72 feet. if the length l of the yard is 18 feet longer than the width w of the yard, what is the area of the yard, in square feet?

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.

The area of the yard is 243 square feet.