Mike would like to enlarge his rectangular front yard which is currently 80 feet by 40 feet. He can only extend the width and length by 5x feet. If x = 7 feet, what will be the increase in area of the front yard?



How can this problem be raised to a higher level of complexity?

Ao = 80 * 40 =3200ft^2 = Initial area.

5X = 5 * 7 = 35ft.

Af = (80 + 35) (40 + 35) = 115 * 75 =
8625ft^2 = Final area.

Ai = 8625 - 3200 = 5425ft^2 = increase
in area.

To solve this problem, we need to find the original area of Mike's front yard and the area after extending the width and length by 5x feet.

First, let's calculate the original area of the front yard by multiplying the length and width:

Original area = length * width = 80 feet * 40 feet = 3200 square feet.

Now, let's calculate the new length and width after extending by 5x feet:

New length = 80 feet + (5 * 7 feet) = 80 feet + 35 feet = 115 feet.

New width = 40 feet + (5 * 7 feet) = 40 feet + 35 feet = 75 feet.

Finally, let's calculate the new area of the front yard by multiplying the new length and width:

New area = new length * new width = 115 feet * 75 feet = 8625 square feet.

To find the increase in area, we subtract the original area from the new area:

Increase in area = New area - Original area = 8625 square feet - 3200 square feet = 5425 square feet.

Therefore, if x = 7 feet, the increase in area of the front yard is 5425 square feet.

To raise the complexity of this problem, we can introduce variables for the length and width of the original front yard instead of using specific numbers. We can also increase the number of times the width and length are extended or introduce other factors that affect the increase in area.