The expression below represents the perimeter, in feet, of Manual’s garden.

15 + 2x + 7 + 15 + 2x + 7

Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Manual’s garden.

The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7.

Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation.

Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length.

The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?

b) The difference, in square feet, between the actual area of Shawn’s garden and the area found using his expression is given as 98 square feet

What is the perimeter?

The perimeter is defined as the sum of all the sides of the figure. Now we have The area in, square feet, of Shawn’s garden is found be calculating 15(2x + 7). Shawn incorrectly says the area can also be found using the expression 30x + 7.

The correct area =15(2x + 7).

= 30x + 105 square feet

The error in Shawn’s expression is

= 15(2x + 7)

= 30x + 7 square feet

Shawn's error was that he Multiplied 15 by 2x only. He didn't Multiply 15 by 7

The difference, in square feet, between the actual area of Shawn’s garden and the area found using his expression is given as

30x + 105 square feet - 30x + 7 square feet

= 30x + 105 - (30x + 7)

= 30x - 30x + 105 - 7

= 98 square feet

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