Question

A garden is 12 feet long by 8 feet wide. The length and width of the garden will each be increased by the same number of feet. The expressions below represent the new length and width of the larger garden Length = (x + 12) ft; width = (x + 8) ft Write an expression that is equivalent to the expression for the PERIMETER the larger garden. Answer : _____________ Write the expression to represent the area of the garden. Answer : ____________

Answer 1

Answer:

A) The expressions for the Perimeter of the garden =

Perimeter = (x + 12)ft + (x +12)ft + (x + 8)ft + (x + 8)ft

Perimeter = 4x + 40 ft

B) The expressions for the Area of the garden =

Area = (x + 12)ft + (x + 8)ft

Area = (x² + 20x + 96)ft²

Step-by-step explanation:

A garden is 12 feet long by 8 feet wide. The length and width of the garden will each be increased by the same number of feet.

The expressions below represent the new length and width of the larger garden Length = (x + 12) ft; width = (x + 8)

A) Perimeter of the Garden

Let us assume that the Garden is rectangular

The formula for Perimeter of the Garden = 2L + 2W

Length = (x + 12)ft

Width = (x + 8)ft

Perimeter = 2(x + 12) ft + 2(x + 8)ft

Perimeter = (x + 12)ft + (x +12)ft + (x + 8)ft + (x + 8)ft

Perimeter = (2x +24 + 2x + 16)ft

Perimeter = (2x + 2x + 24 + 16)ft

Perimeter = 4x + 40 ft

B) The Area of the Garden

The formula for Area of the Garden = L × W

Length = (x + 12)ft

Width = (x + 8)ft

Area = (x + 12)ft + (x + 8)ft

Area = (x² + 8x + 12x + 96)ft²

Area = (x² + 20x + 96)ft²